Edit Profile (opens in new tab) Melvin, Paul M. Co-Author Distance Author ID: melvin.paul-m Published as: Melvin, Paul; Melvin, P. M.; Melvin, P.; Melvin, Paul M. more...less Homepage: http://www.brynmawr.edu/math/people/melvin/ External Links: MGP Documents Indexed: 37 Publications since 1978, including 1 Additional arXiv Preprint Co-Authors: 22 Co-Authors with 30 Joint Publications 449 Co-Co-Authors all top 5 Co-Authors 6 single-authored 9 Kirby, Robion Cromwell 4 Auckly, David R. 4 DeTurck, Dennis M. 4 Gluck, Herman 4 Kim, Hee Jung 4 Komendarczyk, Rafal 4 Ruberman, Daniel 4 Shonkwiler, Clayton 4 Vela-Vick, David Shea 3 Cochran, Thomas (Tim) Daniel 2 Livingston, Charles 2 Morton, Hugh R. 2 Schwartz, Hannah R. 2 Teichner, Peter 1 Friedl, Stefan 1 Hambleton, Ian 1 Hughes, John Forbes 1 Kazez, William H. 1 Mellor, Blake 1 Nuchi, Haggai 1 Shrestha, Sumana 1 Zhang, Xingru all top 5 Serials 4 Inventiones Mathematicae 3 Topology 3 Algebraic & Geometric Topology 2 Communications in Mathematical Physics 2 Journal of the London Mathematical Society. Second Series 2 Mathematische Annalen 2 Proceedings of the American Mathematical Society 1 American Mathematical Monthly 1 Journal of Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Advances in Mathematics 1 Commentarii Mathematici Helvetici 1 Michigan Mathematical Journal 1 Topology and its Applications 1 IMRN. International Mathematics Research Notices 1 Turkish Journal of Mathematics 1 Matemática Contemporânea 1 Geometry & Topology 1 Journal of Topology all top 5 Fields 37 Manifolds and cell complexes (57-XX) 3 Algebraic topology (55-XX) 3 Quantum theory (81-XX) 2 Number theory (11-XX) 2 Nonassociative rings and algebras (17-XX) 2 Differential geometry (53-XX) 2 Fluid mechanics (76-XX) 2 Optics, electromagnetic theory (78-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Computer science (68-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 34 Publications have been cited 478 times in 414 Documents Cited by ▼ Year ▼ The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl\((2,\mathbb{C})\). Zbl 0745.57006 Kirby, Robion; Melvin, Paul 160 1991 The coloured Jones function. Zbl 0845.57007 Melvin, P. M.; Morton, H. R. 47 1995 Dedekind sums, \(\mu\)-invariants and the signature cocycle. Zbl 0809.11027 Kirby, Robion; Melvin, Paul 47 1994 Finite type invariants of 3-manifolds. Zbl 0949.57010 Cochran, Tim D.; Melvin, Paul 17 2000 Abelian invariants of satellite knots. Zbl 0605.57001 Livingston, Charles; Melvin, Paul 15 1985 A geometric interpretation of Milnor’s triple linking numbers. Zbl 1040.57007 Mellor, Blake; Melvin, Paul 14 2003 Stable isotopy in four dimensions. Zbl 1355.57028 Auckly, Dave; Kim, Hee Jung; Melvin, Paul; Ruberman, Daniel 12 2015 The nonuniqueness of Chekanov polynomials of Legendrian knots. Zbl 1084.57009 Melvin, Paul; Shrestha, Sumana 11 2005 Canonical framings for 3-manifolds. Zbl 0947.57020 Kirby, Rob; Melvin, Paul 11 1999 Equivariant corks. Zbl 1382.57010 Auckly, Dave; Kim, Hee Jung; Melvin, Paul; Ruberman, Daniel 11 2017 Slice knots and property R. Zbl 0377.55002 Kirby, Robion; Melvin, Paul 10 1978 Triple linking numbers, ambiguous Hopf invariants and integral formulas for three-component links. Zbl 1194.57007 DeTurck, D.; Gluck, H.; Komendarczyk, R.; Melvin, P.; Shonkwiler, C.; Vela-Vick, D. S. 10 2008 Local surgery formulas for quantum invariants and the Arf invariant. Zbl 1087.57006 Kirby, Robion; Melvin, Paul 9 2004 Algebraic knots are algebraically dependent. Zbl 0522.57007 Livingston, Charles; Melvin, Paul 9 1983 The Smale invariant of a knot. Zbl 0586.57017 Hughes, John F.; Melvin, Paul M. 8 1985 Fibred knots of genus 2 formed by plumbing Hopf bands. Zbl 0576.57008 Melvin, P. M.; Morton, H. R. 8 1986 Quantum cyclotomic orders of 3-manifolds. Zbl 0997.57024 Cochran, Tim D.; Melvin, Paul 8 2001 Generalized Gauss maps and integrals for three-component links: toward higher helicities for magnetic fields and fluid flows. Zbl 1328.57007 DeTurck, Dennis; Gluck, Herman; Komendarczyk, Rafal; Melvin, Paul; Shonkwiler, Clayton; Vela-Vick, David Shea 8 2013 Bordism of diffeomorphisms. Zbl 0418.57014 Melvin, Paul 7 1979 Cohomotopy sets of 4-manifolds. Zbl 1273.57012 Kirby, Robion; Melvin, Paul; Teichner, Peter 7 2012 Evaluations of the 3-manifolds invariants of Witten and Reshetikhin- Turaev for \(sl(2,C)\). Zbl 0756.57006 Kirby, Robion; Melvin, Paul 6 1990 Isotopy of surfaces in 4-manifolds after a single stabilization. Zbl 1457.57041 Auckly, Dave; Kim, Hee Jung; Melvin, Paul; Ruberman, Daniel; Schwartz, Hannah 6 2019 Quantum invariants at the sixth root of unity. Zbl 0779.57007 Kirby, Robion; Melvin, Paul; Zhang, Xingru 5 1993 Tori in the diffeomorphism groups of simply-connected 4-manifolds. Zbl 0486.57016 Melvin, Paul 5 1982 4-manifolds with large symmetry groups. Zbl 0594.57019 Melvin, Paul; Parker, Jeffrey 4 1986 Generalized Gauss maps and integrals for three-component links: toward higher helicities for magnetic fields and fluid flows. II. Zbl 1348.57007 DeTurck, Dennis; Gluck, Herman; Komendarczyk, Rafal; Melvin, Paul; Nuchi, Haggai; Shonkwiler, Clayton; Vela-Vick, David Shea 4 2013 2-sphere bundles over compact surfaces. Zbl 0524.55016 Melvin, Paul 4 1984 Non-smoothable four-manifolds with infinite cyclic fundamental group. Zbl 1153.57019 Friedl, Stefan; Hambleton, Ian; Melvin, Paul; Teichner, Peter 3 2007 On 4-manifolds with singular torus actions. Zbl 0437.57007 Melvin, Paul 3 1981 The Milnor degree of a 3-manifold. Zbl 1198.57008 Cochran, Tim; Melvin, Paul 3 2010 3-dimensional bordism. Zbl 0693.57012 Melvin, P.; Kazez, W. 2 1989 Higher order corks. Zbl 1472.57026 Melvin, Paul; Schwartz, Hannah 2 2021 4-dimensional oriented bordism. Zbl 0561.57008 Melvin, Paul 1 1984 A topological menagerie. Zbl 1094.57021 Melvin, Paul 1 2006 Higher order corks. Zbl 1472.57026 Melvin, Paul; Schwartz, Hannah 2 2021 Isotopy of surfaces in 4-manifolds after a single stabilization. Zbl 1457.57041 Auckly, Dave; Kim, Hee Jung; Melvin, Paul; Ruberman, Daniel; Schwartz, Hannah 6 2019 Equivariant corks. Zbl 1382.57010 Auckly, Dave; Kim, Hee Jung; Melvin, Paul; Ruberman, Daniel 11 2017 Stable isotopy in four dimensions. Zbl 1355.57028 Auckly, Dave; Kim, Hee Jung; Melvin, Paul; Ruberman, Daniel 12 2015 Generalized Gauss maps and integrals for three-component links: toward higher helicities for magnetic fields and fluid flows. Zbl 1328.57007 DeTurck, Dennis; Gluck, Herman; Komendarczyk, Rafal; Melvin, Paul; Shonkwiler, Clayton; Vela-Vick, David Shea 8 2013 Generalized Gauss maps and integrals for three-component links: toward higher helicities for magnetic fields and fluid flows. II. Zbl 1348.57007 DeTurck, Dennis; Gluck, Herman; Komendarczyk, Rafal; Melvin, Paul; Nuchi, Haggai; Shonkwiler, Clayton; Vela-Vick, David Shea 4 2013 Cohomotopy sets of 4-manifolds. Zbl 1273.57012 Kirby, Robion; Melvin, Paul; Teichner, Peter 7 2012 The Milnor degree of a 3-manifold. Zbl 1198.57008 Cochran, Tim; Melvin, Paul 3 2010 Triple linking numbers, ambiguous Hopf invariants and integral formulas for three-component links. Zbl 1194.57007 DeTurck, D.; Gluck, H.; Komendarczyk, R.; Melvin, P.; Shonkwiler, C.; Vela-Vick, D. S. 10 2008 Non-smoothable four-manifolds with infinite cyclic fundamental group. Zbl 1153.57019 Friedl, Stefan; Hambleton, Ian; Melvin, Paul; Teichner, Peter 3 2007 A topological menagerie. Zbl 1094.57021 Melvin, Paul 1 2006 The nonuniqueness of Chekanov polynomials of Legendrian knots. Zbl 1084.57009 Melvin, Paul; Shrestha, Sumana 11 2005 Local surgery formulas for quantum invariants and the Arf invariant. Zbl 1087.57006 Kirby, Robion; Melvin, Paul 9 2004 A geometric interpretation of Milnor’s triple linking numbers. Zbl 1040.57007 Mellor, Blake; Melvin, Paul 14 2003 Quantum cyclotomic orders of 3-manifolds. Zbl 0997.57024 Cochran, Tim D.; Melvin, Paul 8 2001 Finite type invariants of 3-manifolds. Zbl 0949.57010 Cochran, Tim D.; Melvin, Paul 17 2000 Canonical framings for 3-manifolds. Zbl 0947.57020 Kirby, Rob; Melvin, Paul 11 1999 The coloured Jones function. Zbl 0845.57007 Melvin, P. M.; Morton, H. R. 47 1995 Dedekind sums, \(\mu\)-invariants and the signature cocycle. Zbl 0809.11027 Kirby, Robion; Melvin, Paul 47 1994 Quantum invariants at the sixth root of unity. Zbl 0779.57007 Kirby, Robion; Melvin, Paul; Zhang, Xingru 5 1993 The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl\((2,\mathbb{C})\). Zbl 0745.57006 Kirby, Robion; Melvin, Paul 160 1991 Evaluations of the 3-manifolds invariants of Witten and Reshetikhin- Turaev for \(sl(2,C)\). Zbl 0756.57006 Kirby, Robion; Melvin, Paul 6 1990 3-dimensional bordism. Zbl 0693.57012 Melvin, P.; Kazez, W. 2 1989 Fibred knots of genus 2 formed by plumbing Hopf bands. Zbl 0576.57008 Melvin, P. M.; Morton, H. R. 8 1986 4-manifolds with large symmetry groups. Zbl 0594.57019 Melvin, Paul; Parker, Jeffrey 4 1986 Abelian invariants of satellite knots. Zbl 0605.57001 Livingston, Charles; Melvin, Paul 15 1985 The Smale invariant of a knot. Zbl 0586.57017 Hughes, John F.; Melvin, Paul M. 8 1985 2-sphere bundles over compact surfaces. Zbl 0524.55016 Melvin, Paul 4 1984 4-dimensional oriented bordism. Zbl 0561.57008 Melvin, Paul 1 1984 Algebraic knots are algebraically dependent. Zbl 0522.57007 Livingston, Charles; Melvin, Paul 9 1983 Tori in the diffeomorphism groups of simply-connected 4-manifolds. Zbl 0486.57016 Melvin, Paul 5 1982 On 4-manifolds with singular torus actions. Zbl 0437.57007 Melvin, Paul 3 1981 Bordism of diffeomorphisms. Zbl 0418.57014 Melvin, Paul 7 1979 Slice knots and property R. Zbl 0377.55002 Kirby, Robion; Melvin, Paul 10 1978 all cited Publications top 5 cited Publications all top 5 Cited by 454 Authors 13 Le, Thang Tu Quoc 10 Melvin, Paul M. 10 Murakami, Hitoshi 8 Kauffman, Louis Hirsch 8 Komendarczyk, Rafal 7 Rozansky, Lev 7 Sabloff, Joshua M. 6 Costantino, Francesco 6 Davis, Christopher William 6 Garoufalidis, Stavros 6 Gilmer, Patrick M. 6 Gukov, Sergei 6 Massuyeau, Gwénaël 6 Ruberman, Daniel 5 Cochran, Thomas (Tim) Daniel 5 Gompf, Robert E. 5 Ohtsuki, Tomotada 5 Park, Sunghyuk 5 Putrov, Pavel 5 Ray, Arunima 5 Takase, Masamichi 5 Takata, Toshie 4 Chen, Qi 4 Habiro, Kazuo 4 Hikami, Kazuhiro 4 Hillman, Jonathan Arthur 4 Kirby, Robion Cromwell 4 Koytcheff, Robin 4 Lawrence, Ruth J. 4 Murakami, Jun 4 Pinzón-Caicedo, Juanita 4 Sati, Hisham 4 Shonkwiler, Clayton 4 Spreer, Jonathan 4 Tange, Motoo 3 Auckly, David R. 3 Beliakova, Anna 3 Blanchet, Christian 3 Burton, Benjamin A. 3 Chae, John 3 Conway, Anthony 3 Ekholm, Tobias 3 Frohman, Charles D. 3 Geer, Nathan 3 Gelca, Răzvan 3 Gluck, Herman 3 Hansen, Søren Kold 3 Harvey, Shelly L. 3 Hedden, Matthew 3 Ito, Tetsuya 3 Kania-Bartoszyńska, Joanna 3 Kim, Min Hoon 3 Kucharski, Piotr 3 Maria, Clément 3 Masbaum, Gregor 3 Ng, Lenhard L. 3 Patureau-Mirand, Bertrand 3 Piccirillo, Lisa 3 Sawin, Stephen F. 3 Schreiber, Urs 3 Schwartz, Hannah R. 3 Sułkowski, Piotr 3 Traynor, Lisa 3 Yokota, Yoshiyuki 2 Akhmet’ev, Pëtr Mikhaĭlovich 2 Amundsen, Jonah 2 Anosova, Olga 2 Baker, Kenneth L. 2 Bar-Natan, Dror 2 Bayad, Abdelmejid 2 Baykur, Refik İnanç 2 Berest, Yuri Yu. 2 Borodzik, Maciej 2 Bright, Matthew 2 Burrin, Claire 2 Bytsenko, Andrei A. 2 Cattabriga, Alessia 2 Cattaneo, Alberto Sergio 2 Champanerkar, Abhijit 2 Chung, Hee-Joong 2 Cohen, Frederick Ronald 2 DeTurck, Dennis M. 2 Etnyre, John B. 2 Feller, Peter 2 Fuji, Hiroyuki 2 Funar, Louis 2 Gang, Dongmin 2 Gruen, Angus 2 Horvat, Eva 2 Jeffrey, Lisa Claire 2 Jun, Byungheup 2 Kalfagianni, Efstratia 2 Kalmár, Boldizsár 2 Kawauchi, Akio 2 Kim, Hee Jung 2 Kofman, Ilya 2 Konno, Hokuto 2 Kurlin, Vitaliy 2 Lee, Jungyun 2 Leidy, Constance ...and 354 more Authors all top 5 Cited in 105 Serials 39 Journal of Knot Theory and its Ramifications 29 Algebraic & Geometric Topology 25 Communications in Mathematical Physics 20 Transactions of the American Mathematical Society 20 Geometry & Topology 18 Topology and its Applications 13 Journal of Topology 12 Mathematical Proceedings of the Cambridge Philosophical Society 11 Proceedings of the American Mathematical Society 10 Advances in Mathematics 10 Journal of High Energy Physics 9 Journal of Mathematical Physics 8 Mathematische Annalen 8 International Journal of Mathematics 7 Duke Mathematical Journal 7 Inventiones Mathematicae 6 Bulletin of the London Mathematical Society 6 Geometriae Dedicata 6 Quantum Topology 5 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Journal of Geometry and Physics 4 Journal of Pure and Applied Algebra 4 Mathematische Zeitschrift 4 Pacific Journal of Mathematics 3 Communications in Algebra 3 Israel Journal of Mathematics 3 Letters in Mathematical Physics 3 Nuclear Physics. B 3 Rocky Mountain Journal of Mathematics 3 Annales de l’Institut Fourier 3 Journal of Number Theory 3 Manuscripta Mathematica 3 Osaka Journal of Mathematics 3 Experimental Mathematics 3 Journal of Mathematical Sciences (New York) 3 Journal of the European Mathematical Society (JEMS) 3 Winter Braids Lecture Notes 2 Theoretical and Mathematical Physics 2 Chaos, Solitons and Fractals 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Archiv der Mathematik 2 Canadian Journal of Mathematics 2 Journal of Algebra 2 Journal of Differential Geometry 2 Journal für die Reine und Angewandte Mathematik 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Bulletin of the American Mathematical Society. New Series 2 Chinese Science Bulletin 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Selecta Mathematica. New Series 2 Annales Henri Poincaré 1 Modern Physics Letters A 1 International Journal of Modern Physics A 1 Bulletin of the Australian Mathematical Society 1 Discrete Mathematics 1 Physics Letters. B 1 Arkiv för Matematik 1 Reviews in Mathematical Physics 1 Fortschritte der Physik 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Mathematica 1 Acta Mathematica Vietnamica 1 Bulletin de la Société Mathématique de France 1 Commentarii Mathematici Helvetici 1 Compositio Mathematica 1 Fundamenta Mathematicae 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of the London Mathematical Society. Second Series 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Quaestiones Mathematicae 1 Tôhoku Mathematical Journal. Second Series 1 European Journal of Combinatorics 1 Bulletin of the Korean Mathematical Society 1 Revista Matemática Iberoamericana 1 Journal of the American Mathematical Society 1 Computational Mathematics and Mathematical Physics 1 Annals of Physics 1 Linear Algebra and its Applications 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Indagationes Mathematicae. New Series 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Revista Matemática Complutense 1 Acta Mathematica Sinica. English Series 1 Communications in Contemporary Mathematics 1 Foundations of Computational Mathematics 1 Journal of the Australian Mathematical Society 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Milan Journal of Mathematics 1 Journal of Algebra and its Applications 1 Mediterranean Journal of Mathematics 1 Foundations of Physics 1 Oberwolfach Reports 1 Proceedings of the Steklov Institute of Mathematics 1 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM ...and 5 more Serials all top 5 Cited in 37 Fields 359 Manifolds and cell complexes (57-XX) 71 Quantum theory (81-XX) 41 Nonassociative rings and algebras (17-XX) 32 Differential geometry (53-XX) 29 Number theory (11-XX) 29 Algebraic topology (55-XX) 22 Global analysis, analysis on manifolds (58-XX) 19 Group theory and generalizations (20-XX) 17 Category theory; homological algebra (18-XX) 16 Associative rings and algebras (16-XX) 12 Relativity and gravitational theory (83-XX) 11 Algebraic geometry (14-XX) 7 Fluid mechanics (76-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Combinatorics (05-XX) 5 Topological groups, Lie groups (22-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Computer science (68-XX) 4 \(K\)-theory (19-XX) 3 Optics, electromagnetic theory (78-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Partial differential equations (35-XX) 2 Functional analysis (46-XX) 2 Mechanics of particles and systems (70-XX) 1 General and overarching topics; collections (00-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Geometry (51-XX) 1 Statistics (62-XX) Citations by Year