Edit Profile (opens in new tab) Thompson, Abigail A. Co-Author Distance Author ID: thompson.abigail-a Published as: Thompson, Abigail; Thompson, Abigail A.; Thompson, A. more...less Homepage: https://www.math.ucdavis.edu/~thompson/ External Links: Women in Mathematics · MacTutor · MGP · Wikidata Documents Indexed: 44 Publications since 1987, including 4 Additional arXiv Preprints Co-Authors: 12 Co-Authors with 29 Joint Publications 269 Co-Co-Authors all top 5 Co-Authors 15 single-authored 16 Scharlemann, Martin G. 7 Hass, Joel 3 Tsvietkova, Anastasiia 2 Kirby, Robion Cromwell 2 Rubinstein, J. Hyam 1 Goda, Hiroshi 1 Gompf, Robert E. 1 Johnson, Jesse Edward 1 Meier, Jeffrey 1 Menasco, William W. 1 Thurston, William Paul 1 Zupan, Alexander all top 5 Serials 5 Topology 3 Proceedings of the American Mathematical Society 3 Journal of Knot Theory and its Ramifications 3 Geometry & Topology 2 Illinois Journal of Mathematics 2 Journal of Differential Geometry 2 Mathematische Annalen 2 Mathematical Research Letters 2 Algebraic & Geometric Topology 1 Bulletin of the London Mathematical Society 1 Commentarii Mathematici Helvetici 1 Geometriae Dedicata 1 Indiana University Mathematics Journal 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Topology and its Applications 1 IMRN. International Mathematics Research Notices 1 Proceedings of the National Academy of Sciences of the United States of America 1 Bulletin of the American Mathematical Society. New Series 1 Notices of the American Mathematical Society 1 New Zealand Journal of Mathematics all top 5 Fields 41 Manifolds and cell complexes (57-XX) 2 Combinatorics (05-XX) 2 Differential geometry (53-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 35 Publications have been cited 465 times in 347 Documents Cited by ▼ Year ▼ Thin position for 3-manifolds. Zbl 0818.57013 Scharlemann, Martin; Thompson, Abigail 74 1994 Thin position and the recognition problem for \(S^ 3\). Zbl 0849.57009 Thompson, Abigail 62 1994 Heegaard splittings of \((\text{surface})\times I\) are standard. Zbl 0814.57010 Scharlemann, Martin; Thompson, Abigail 50 1993 Link genus and the Conway moves. Zbl 0693.57004 Scharlemann, Martin; Thompson, Abigail 41 1989 Thin position and bridge number for knots in the 3-sphere. Zbl 0867.57009 Thompson, Abigail 30 1997 Thin position and Heegaard splittings of the 3-sphere. Zbl 0820.57005 Scharlemann, Martin; Thompson, Abigail 21 1994 Unknotting number, genus and companion tori. Zbl 0616.57003 Scharlemann, Martin; Thompson, Abigail 20 1988 Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures. Zbl 1214.57008 Gompf, Robert E.; Scharlemann, Martin; Thompson, Abigail 17 2010 Levelling an unknotting tunnel. Zbl 0958.57007 Goda, Hiroshi; Scharlemann, Martin; Thompson, Abigail 15 2000 The disjoint curve property and genus 2 manifolds. Zbl 0935.57022 Thompson, Abigail 15 1999 Finding disjoint Seifert surfaces. Zbl 0654.57005 Scharlemann, Martin; Thompson, Abigail 14 1988 Stabilization of Heegaard splittings. Zbl 1177.57018 Hass, Joel; Thompson, Abigail; Thurston, William 14 2009 Detecting unknotted graphs in 3-space. Zbl 0751.05033 Scharlemann, Martin; Thompson, Abigail 13 1991 Unknotting tunnels and Seifert surfaces. Zbl 1047.57008 Scharlemann, Martin; Thompson, Abigail 11 2003 On tunnel number one knots that are not \((1, n)\). Zbl 1218.57008 Johnson, Jesse; Thompson, Abigail 10 2011 On the additivity of knot width. Zbl 1207.57016 Scharlemann, Martin; Thompson, Abigail 6 2004 Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds. Zbl 1071.57015 Scharlemann, Martin; Thompson, Abigail 5 2005 Property P for the band-connect sum of two knots. Zbl 0628.57005 Thompson, Abigail 5 1987 Knots with unknotting number one are determined by their complements. Zbl 0677.57006 Thompson, Abigail 5 1989 A new invariant of 4-manifolds. Zbl 1421.57031 Kirby, Robion; Thompson, Abigail 5 2018 Surgery on a knot in (surface \(\times I\)). Zbl 1197.57011 Scharlemann, Martin; Thompson, Abigail A. 5 2009 A polynomial invariant of graphs in 3-manifolds. Zbl 0773.57002 Thompson, Abigail 4 1992 The number of surfaces of fixed genus in an alternating link complement. Zbl 1405.57014 Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia 4 2017 Algorithmic recognition of 3-manifolds. Zbl 0890.57027 Thompson, Abigail 3 1998 Neon bulbs and the unknotting of arcs in manifolds. Zbl 0886.57003 Hass, Joel; Thompson, Abigail 2 1997 Thurston norm minimizing surfaces and skein trees for links in \(S^ 3\). Zbl 0686.57004 Thompson, Abigail 2 1989 A necessary and sufficient condition for a 3-manifold to have Heegaard genus one. Zbl 0694.57006 Hass, Joel; Thompson, Abigail 2 1989 Compressing handlebodies with holes. Zbl 0683.57004 Menasco, W.; Thompson, A. 2 1989 Thinning genus two Heegaard spines in \(S^ 3\). Zbl 1048.57002 Scharlemann, Martin; Thompson, Abigail 2 2003 Invariants of curves in \(\mathbb RP^2\) and \(\mathbb R^2\). Zbl 1128.53010 Thompson, Abigail 1 2006 3-manifolds with Heegaard splittings of distance two. Zbl 1282.57026 Rubinstein, J. Hyam; Thompson, Abigail 1 2013 Tori and Heegaard splittings. Zbl 1367.57009 Thompson, Abigail 1 2016 Knots and \(k\)-width. Zbl 1189.57005 Hass, Joel; Rubinstein, J. Hyam; Thompson, Abigail 1 2009 Tangle decompositions of alternating link complements. Zbl 1482.57004 Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia 1 2021 Alternating links have at most polynomially many Seifert surfaces of fixed genus. Zbl 1467.57004 Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia 1 2021 Tangle decompositions of alternating link complements. Zbl 1482.57004 Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia 1 2021 Alternating links have at most polynomially many Seifert surfaces of fixed genus. Zbl 1467.57004 Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia 1 2021 A new invariant of 4-manifolds. Zbl 1421.57031 Kirby, Robion; Thompson, Abigail 5 2018 The number of surfaces of fixed genus in an alternating link complement. Zbl 1405.57014 Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia 4 2017 Tori and Heegaard splittings. Zbl 1367.57009 Thompson, Abigail 1 2016 3-manifolds with Heegaard splittings of distance two. Zbl 1282.57026 Rubinstein, J. Hyam; Thompson, Abigail 1 2013 On tunnel number one knots that are not \((1, n)\). Zbl 1218.57008 Johnson, Jesse; Thompson, Abigail 10 2011 Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures. Zbl 1214.57008 Gompf, Robert E.; Scharlemann, Martin; Thompson, Abigail 17 2010 Stabilization of Heegaard splittings. Zbl 1177.57018 Hass, Joel; Thompson, Abigail; Thurston, William 14 2009 Surgery on a knot in (surface \(\times I\)). Zbl 1197.57011 Scharlemann, Martin; Thompson, Abigail A. 5 2009 Knots and \(k\)-width. Zbl 1189.57005 Hass, Joel; Rubinstein, J. Hyam; Thompson, Abigail 1 2009 Invariants of curves in \(\mathbb RP^2\) and \(\mathbb R^2\). Zbl 1128.53010 Thompson, Abigail 1 2006 Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds. Zbl 1071.57015 Scharlemann, Martin; Thompson, Abigail 5 2005 On the additivity of knot width. Zbl 1207.57016 Scharlemann, Martin; Thompson, Abigail 6 2004 Unknotting tunnels and Seifert surfaces. Zbl 1047.57008 Scharlemann, Martin; Thompson, Abigail 11 2003 Thinning genus two Heegaard spines in \(S^ 3\). Zbl 1048.57002 Scharlemann, Martin; Thompson, Abigail 2 2003 Levelling an unknotting tunnel. Zbl 0958.57007 Goda, Hiroshi; Scharlemann, Martin; Thompson, Abigail 15 2000 The disjoint curve property and genus 2 manifolds. Zbl 0935.57022 Thompson, Abigail 15 1999 Algorithmic recognition of 3-manifolds. Zbl 0890.57027 Thompson, Abigail 3 1998 Thin position and bridge number for knots in the 3-sphere. Zbl 0867.57009 Thompson, Abigail 30 1997 Neon bulbs and the unknotting of arcs in manifolds. Zbl 0886.57003 Hass, Joel; Thompson, Abigail 2 1997 Thin position for 3-manifolds. Zbl 0818.57013 Scharlemann, Martin; Thompson, Abigail 74 1994 Thin position and the recognition problem for \(S^ 3\). Zbl 0849.57009 Thompson, Abigail 62 1994 Thin position and Heegaard splittings of the 3-sphere. Zbl 0820.57005 Scharlemann, Martin; Thompson, Abigail 21 1994 Heegaard splittings of \((\text{surface})\times I\) are standard. Zbl 0814.57010 Scharlemann, Martin; Thompson, Abigail 50 1993 A polynomial invariant of graphs in 3-manifolds. Zbl 0773.57002 Thompson, Abigail 4 1992 Detecting unknotted graphs in 3-space. Zbl 0751.05033 Scharlemann, Martin; Thompson, Abigail 13 1991 Link genus and the Conway moves. Zbl 0693.57004 Scharlemann, Martin; Thompson, Abigail 41 1989 Knots with unknotting number one are determined by their complements. Zbl 0677.57006 Thompson, Abigail 5 1989 Thurston norm minimizing surfaces and skein trees for links in \(S^ 3\). Zbl 0686.57004 Thompson, Abigail 2 1989 A necessary and sufficient condition for a 3-manifold to have Heegaard genus one. Zbl 0694.57006 Hass, Joel; Thompson, Abigail 2 1989 Compressing handlebodies with holes. Zbl 0683.57004 Menasco, W.; Thompson, A. 2 1989 Unknotting number, genus and companion tori. Zbl 0616.57003 Scharlemann, Martin; Thompson, Abigail 20 1988 Finding disjoint Seifert surfaces. Zbl 0654.57005 Scharlemann, Martin; Thompson, Abigail 14 1988 Property P for the band-connect sum of two knots. Zbl 0628.57005 Thompson, Abigail 5 1987 all cited Publications top 5 cited Publications all top 5 Cited by 298 Authors 22 Scharlemann, Martin G. 16 Tomova, Maggy 13 Taylor, Scott A. 12 Lei, Fengchun 11 Thompson, Abigail A. 10 Li, Tao 10 Qiu, Ruifeng 9 Bachman, David 9 Kobayashi, Tsuyoshi 9 Schultens, Jennifer 8 Lee, Junghoon 8 Ozawa, Makoto 8 Zupan, Alexander 7 Lackenby, Marc 7 Moriah, Yoav 7 Rubinstein, J. Hyam 7 Sedgwick, Eric 7 Yang, Guoqiu 7 Zou, Yanqing 6 Blair, Ryan C. 6 Cho, Sangbum 6 Johnson, Jesse Edward 5 Burton, Benjamin A. 5 Du, Kun 5 Li, Fengling 5 Schleimer, Saul 4 Goda, Hiroshi 4 Gordon, Cameron McA. 4 Hass, Joel 4 Huh, Youngsik 4 Kalfagianni, Efstratia 4 Luecke, John 4 McCullough, Darryl 4 Meier, Jeffrey 4 Moore, Allison H. 4 Shimokawa, Koya 4 Taniyama, Kouki 3 Baker, Kenneth L. 3 Bleiler, Steven A. 3 Derby-Talbot, Ryan 3 E, Qiang 3 Eudave-Muñoz, Mario 3 Gompf, Robert E. 3 Guo, Qilong 3 Hayashi, Chuichiro 3 Ishihara, Kai 3 Jaco, William H. 3 Jang, Yeonhee 3 Kang, Ensil 3 Kim, Jungsoo 3 Koda, Yuya 3 Lidman, Tye 3 Lutz, Frank Hagen 3 Miller, Maggie 3 Motegi, Kimihiko 3 Purcell, Jessica Shepherd 3 Rieck, Yo’av 3 Takao, Kazuto 3 Vazquez, Mariel 3 Wagner, Uli 2 Agol, Ian 2 Balm, Cheryl Jaeger 2 Benedetti, Riccardo 2 Campisi, Marion Moore 2 Carmesin, Johannes 2 Darcy, Isabel K. 2 Dasbach, Oliver T. 2 Deruelle, Arnaud 2 Freedman, Michael Hartley 2 Friedl, Stefan 2 Frigerio, Roberto 2 Gao, Xutao 2 Heath, Daniel J. 2 Huszár, Kristóf 2 Ido, Ayako 2 Islambouli, Gabriel 2 Ivanov, Sergei Vladimirovich 2 Jang, Hee Jeong 2 Lee, Sang Youl 2 Lee, Sangjin 2 Li, Yang 2 Liang, Liang 2 Lin, Xiao-Song 2 Mangum, Brian S. 2 Manturov, Vassiliĭ Olegovich 2 Matsuda, Hiroshi 2 Namazi, Hossein 2 Ni, Yi 2 Nikkuni, Ryo 2 Portmann, Fabian 2 Renard, Claire 2 Sakasai, Takuya 2 Segerman, Henry 2 Sok, Jérémy 2 Solovej, Jan Philip 2 Takioka, Hideo 2 Tillmann, Stephan 2 Tsvietkova, Anastasiia 2 Watson, Liam 2 Wilson, Robin Todd ...and 198 more Authors all top 5 Cited in 81 Serials 49 Algebraic & Geometric Topology 44 Topology and its Applications 42 Journal of Knot Theory and its Ramifications 25 Geometry & Topology 24 Transactions of the American Mathematical Society 19 Proceedings of the American Mathematical Society 14 Geometriae Dedicata 10 Mathematische Annalen 5 Mathematical Proceedings of the Cambridge Philosophical Society 4 Inventiones Mathematicae 4 Journal of Topology 4 Winter Braids Lecture Notes 3 Chaos, Solitons and Fractals 3 Advances in Mathematics 3 Duke Mathematical Journal 3 Journal of the London Mathematical Society. Second Series 3 Michigan Mathematical Journal 3 Osaka Journal of Mathematics 3 Chinese Annals of Mathematics. Series B 3 Bulletin of the American Mathematical Society. New Series 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Journal of the Mathematical Society of Japan 2 Pacific Journal of Mathematics 2 Tokyo Journal of Mathematics 2 Discrete & Computational Geometry 2 Geometric and Functional Analysis. GAFA 2 New Zealand Journal of Mathematics 2 Experimental Mathematics 2 St. Petersburg Mathematical Journal 2 Acta Mathematica Sinica. English Series 2 Science China. Mathematics 2 Journal of Singularities 1 Discrete Mathematics 1 Houston Journal of Mathematics 1 Israel Journal of Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Mathematical Physics 1 Nuclear Physics. B 1 Periodica Mathematica Hungarica 1 Mathematics of Computation 1 Cahiers de Topologie et Géométrie Différentielle Catégoriques 1 Compositio Mathematica 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of Combinatorial Theory. Series A 1 Journal of Differential Geometry 1 Journal of Graph Theory 1 Journal für die Reine und Angewandte Mathematik 1 Transactions of the Moscow Mathematical Society 1 European Journal of Combinatorics 1 Annals of Pure and Applied Logic 1 Journal of the American Mathematical Society 1 Forum Mathematicum 1 Sugaku Expositions 1 International Journal of Mathematics 1 The Journal of Geometric Analysis 1 L’Enseignement Mathématique. 2e Série 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Topology Proceedings 1 The New York Journal of Mathematics 1 Selecta Mathematica. New Series 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Revista Matemática Complutense 1 Journal of the European Mathematical Society (JEMS) 1 Journal of the Australian Mathematical Society 1 Acta Mathematica Scientia. Series B. (English Edition) 1 JP Journal of Geometry and Topology 1 Oberwolfach Reports 1 Chebyshevskiĭ Sbornik 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Physics A: Mathematical and Theoretical 1 Quantum Topology 1 Journal of Mathematical Research with Applications 1 Axioms 1 Proceedings of the American Mathematical Society. Series B 1 Journal of Applied and Computational Topology 1 Peking Mathematical Journal 1 SN Partial Differential Equations and Applications 1 CGT. Computing in Geometry and Topology all top 5 Cited in 27 Fields 340 Manifolds and cell complexes (57-XX) 17 Combinatorics (05-XX) 11 Computer science (68-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Group theory and generalizations (20-XX) 6 Convex and discrete geometry (52-XX) 6 Biology and other natural sciences (92-XX) 4 Algebraic topology (55-XX) 3 Quantum theory (81-XX) 2 History and biography (01-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Fluid mechanics (76-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.