Edit Profile (opens in new tab) Thompson, Abigail A. Compute Distance To: Compute 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: 39 Publications since 1987 Co-Authors: 10 Co-Authors with 27 Joint Publications 210 Co-Co-Authors all top 5 Co-Authors 12 single-authored 15 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 Menasco, William W. 1 Thurston, William Paul 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 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 1 Mathematical Research Letters all top 5 Fields 37 Manifolds and cell complexes (57-XX) 2 Differential geometry (53-XX) 1 Combinatorics (05-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 33 Publications have been cited 423 times in 314 Documents Cited by ▼ Year ▼ Thin position for 3-manifolds. Zbl 0818.57013Scharlemann, Martin; Thompson, Abigail 65 1994 Thin position and the recognition problem for \(S^ 3\). Zbl 0849.57009Thompson, Abigail 57 1994 Heegaard splittings of \((\text{surface})\times I\) are standard. Zbl 0814.57010Scharlemann, Martin; Thompson, Abigail 48 1993 Link genus and the Conway moves. Zbl 0693.57004Scharlemann, Martin; Thompson, Abigail 37 1989 Thin position and bridge number for knots in the 3-sphere. Zbl 0867.57009Thompson, Abigail 28 1997 Unknotting number, genus and companion tori. Zbl 0616.57003Scharlemann, Martin; Thompson, Abigail 20 1988 Thin position and Heegaard splittings of the 3-sphere. Zbl 0820.57005Scharlemann, Martin; Thompson, Abigail 19 1994 The disjoint curve property and genus 2 manifolds. Zbl 0935.57022Thompson, Abigail 15 1999 Finding disjoint Seifert surfaces. Zbl 0654.57005Scharlemann, Martin; Thompson, Abigail 14 1988 Levelling an unknotting tunnel. Zbl 0958.57007Goda, Hiroshi; Scharlemann, Martin; Thompson, Abigail 14 2000 Stabilization of Heegaard splittings. Zbl 1177.57018Hass, Joel; Thompson, Abigail; Thurston, William 14 2009 Detecting unknotted graphs in 3-space. Zbl 0751.05033Scharlemann, Martin; Thompson, Abigail 12 1991 On tunnel number one knots that are not \((1, n)\). Zbl 1218.57008Johnson, Jesse; Thompson, Abigail 10 2011 Unknotting tunnels and Seifert surfaces. Zbl 1047.57008Scharlemann, Martin; Thompson, Abigail 10 2003 Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures. Zbl 1214.57008Gompf, Robert E.; Scharlemann, Martin; Thompson, Abigail 10 2010 On the additivity of knot width. Zbl 1207.57016Scharlemann, Martin; Thompson, Abigail 5 2004 Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds. Zbl 1071.57015Scharlemann, Martin; Thompson, Abigail 5 2005 Knots with unknotting number one are determined by their complements. Zbl 0677.57006Thompson, Abigail 5 1989 Surgery on a knot in (surface \(\times I\)). Zbl 1197.57011Scharlemann, Martin; Thompson, Abigail A. 5 2009 Property P for the band-connect sum of two knots. Zbl 0628.57005Thompson, Abigail 5 1987 Algorithmic recognition of 3-manifolds. Zbl 0890.57027Thompson, Abigail 3 1998 The number of surfaces of fixed genus in an alternating link complement. Zbl 1405.57014Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia 3 2017 A polynomial invariant of graphs in 3-manifolds. Zbl 0773.57002Thompson, Abigail 3 1992 A new invariant of 4-manifolds. Zbl 1421.57031Kirby, Robion; Thompson, Abigail 3 2018 Thinning genus two Heegaard spines in \(S^ 3\). Zbl 1048.57002Scharlemann, Martin; Thompson, Abigail 2 2003 Compressing handlebodies with holes. Zbl 0683.57004Menasco, W.; Thompson, A. 2 1989 Thurston norm minimizing surfaces and skein trees for links in \(S^ 3\). Zbl 0686.57004Thompson, Abigail 2 1989 A necessary and sufficient condition for a 3-manifold to have Heegaard genus one. Zbl 0694.57006Hass, Joel; Thompson, Abigail 2 1989 3-manifolds with Heegaard splittings of distance two. Zbl 1282.57026Rubinstein, J. Hyam; Thompson, Abigail 1 2013 Neon bulbs and the unknotting of arcs in manifolds. Zbl 0886.57003Hass, Joel; Thompson, Abigail 1 1997 Invariants of curves in \(\mathbb RP^2\) and \(\mathbb R^2\). Zbl 1128.53010Thompson, Abigail 1 2006 Tangle decompositions of alternating link complements. Zbl 1482.57004Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia 1 2021 Knots and \(k\)-width. Zbl 1189.57005Hass, Joel; Rubinstein, J. Hyam; Thompson, Abigail 1 2009 Tangle decompositions of alternating link complements. Zbl 1482.57004Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia 1 2021 A new invariant of 4-manifolds. Zbl 1421.57031Kirby, Robion; Thompson, Abigail 3 2018 The number of surfaces of fixed genus in an alternating link complement. Zbl 1405.57014Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia 3 2017 3-manifolds with Heegaard splittings of distance two. Zbl 1282.57026Rubinstein, J. Hyam; Thompson, Abigail 1 2013 On tunnel number one knots that are not \((1, n)\). Zbl 1218.57008Johnson, Jesse; Thompson, Abigail 10 2011 Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures. Zbl 1214.57008Gompf, Robert E.; Scharlemann, Martin; Thompson, Abigail 10 2010 Stabilization of Heegaard splittings. Zbl 1177.57018Hass, Joel; Thompson, Abigail; Thurston, William 14 2009 Surgery on a knot in (surface \(\times I\)). Zbl 1197.57011Scharlemann, Martin; Thompson, Abigail A. 5 2009 Knots and \(k\)-width. Zbl 1189.57005Hass, Joel; Rubinstein, J. Hyam; Thompson, Abigail 1 2009 Invariants of curves in \(\mathbb RP^2\) and \(\mathbb R^2\). Zbl 1128.53010Thompson, Abigail 1 2006 Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds. Zbl 1071.57015Scharlemann, Martin; Thompson, Abigail 5 2005 On the additivity of knot width. Zbl 1207.57016Scharlemann, Martin; Thompson, Abigail 5 2004 Unknotting tunnels and Seifert surfaces. Zbl 1047.57008Scharlemann, Martin; Thompson, Abigail 10 2003 Thinning genus two Heegaard spines in \(S^ 3\). Zbl 1048.57002Scharlemann, Martin; Thompson, Abigail 2 2003 Levelling an unknotting tunnel. Zbl 0958.57007Goda, Hiroshi; Scharlemann, Martin; Thompson, Abigail 14 2000 The disjoint curve property and genus 2 manifolds. Zbl 0935.57022Thompson, Abigail 15 1999 Algorithmic recognition of 3-manifolds. Zbl 0890.57027Thompson, Abigail 3 1998 Thin position and bridge number for knots in the 3-sphere. Zbl 0867.57009Thompson, Abigail 28 1997 Neon bulbs and the unknotting of arcs in manifolds. Zbl 0886.57003Hass, Joel; Thompson, Abigail 1 1997 Thin position for 3-manifolds. Zbl 0818.57013Scharlemann, Martin; Thompson, Abigail 65 1994 Thin position and the recognition problem for \(S^ 3\). Zbl 0849.57009Thompson, Abigail 57 1994 Thin position and Heegaard splittings of the 3-sphere. Zbl 0820.57005Scharlemann, Martin; Thompson, Abigail 19 1994 Heegaard splittings of \((\text{surface})\times I\) are standard. Zbl 0814.57010Scharlemann, Martin; Thompson, Abigail 48 1993 A polynomial invariant of graphs in 3-manifolds. Zbl 0773.57002Thompson, Abigail 3 1992 Detecting unknotted graphs in 3-space. Zbl 0751.05033Scharlemann, Martin; Thompson, Abigail 12 1991 Link genus and the Conway moves. Zbl 0693.57004Scharlemann, Martin; Thompson, Abigail 37 1989 Knots with unknotting number one are determined by their complements. Zbl 0677.57006Thompson, Abigail 5 1989 Compressing handlebodies with holes. Zbl 0683.57004Menasco, W.; Thompson, A. 2 1989 Thurston norm minimizing surfaces and skein trees for links in \(S^ 3\). Zbl 0686.57004Thompson, Abigail 2 1989 A necessary and sufficient condition for a 3-manifold to have Heegaard genus one. Zbl 0694.57006Hass, Joel; Thompson, Abigail 2 1989 Unknotting number, genus and companion tori. Zbl 0616.57003Scharlemann, Martin; Thompson, Abigail 20 1988 Finding disjoint Seifert surfaces. Zbl 0654.57005Scharlemann, Martin; Thompson, Abigail 14 1988 Property P for the band-connect sum of two knots. Zbl 0628.57005Thompson, Abigail 5 1987 all cited Publications top 5 cited Publications all top 5 Cited by 270 Authors 20 Scharlemann, Martin G. 15 Tomova, Maggy 12 Lei, Fengchun 11 Thompson, Abigail A. 10 Qiu, Ruifeng 10 Taylor, Scott A. 9 Bachman, David 9 Kobayashi, Tsuyoshi 9 Schultens, Jennifer 8 Li, Tao 8 Ozawa, Makoto 7 Lee, Junghoon 7 Sedgwick, Eric 7 Yang, Guoqiu 7 Zou, Yanqing 6 Cho, Sangbum 6 Johnson, Jesse Edward 6 Lackenby, Marc 6 Moriah, Yoav 6 Rubinstein, J. Hyam 6 Zupan, Alexander 5 Blair, Ryan C. 5 Burton, Benjamin A. 5 Du, Kun 5 Li, Fengling 4 Goda, Hiroshi 4 Gordon, Cameron McA. 4 Hass, Joel 4 Kalfagianni, Efstratia 4 Luecke, John 4 McCullough, Darryl 4 Schleimer, Saul 4 Shimokawa, Koya 4 Taniyama, Kouki 3 Bleiler, Steven A. 3 Derby-Talbot, Ryan 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 Lutz, Frank Hagen 3 Meier, Jeffrey 3 Miller, Maggie 3 Moore, Allison H. 3 Motegi, Kimihiko 3 Rieck, Yo’av 3 Takao, Kazuto 3 Vazquez, Mariel 2 Agol, Ian 2 Baker, Kenneth L. 2 Balm, Cheryl Jaeger 2 Benedetti, Riccardo 2 Carmesin, Johannes 2 Darcy, Isabel K. 2 Dasbach, Oliver T. 2 Deruelle, Arnaud 2 E., Qiang 2 Eudave-Muñoz, Mario 2 Frigerio, Roberto 2 Gao, Xutao 2 Heath, Daniel J. 2 Huh, Youngsik 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 Lidman, Tye 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 Sok, Jérémy 2 Solovej, Jan Philip 2 Takioka, Hideo 2 Tsvietkova, Anastasiia 2 Wagner, Uli 1 Appleboim, Eli 1 Armas-Sanabria, Lorena 1 Askitas, Nikos 1 Ba, Idrissa 1 Bart, Anneke 1 Barthel, Senja 1 Baykur, Refik İnanç 1 Belousov, Yu. S. 1 Berge, John ...and 170 more Authors all top 5 Cited in 70 Serials 46 Algebraic & Geometric Topology 44 Topology and its Applications 40 Journal of Knot Theory and its Ramifications 24 Transactions of the American Mathematical Society 24 Geometry & Topology 19 Proceedings of the American Mathematical Society 12 Geometriae Dedicata 9 Mathematische Annalen 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Inventiones Mathematicae 3 Chaos, Solitons and Fractals 3 Advances in Mathematics 3 Osaka Journal of Mathematics 3 Chinese Annals of Mathematics. Series B 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Winter Braids Lecture Notes 2 Duke Mathematical Journal 2 Michigan Mathematical Journal 2 Pacific Journal of Mathematics 2 Tokyo Journal of Mathematics 2 Discrete & Computational Geometry 2 Geometric and Functional Analysis. GAFA 2 Bulletin of the American Mathematical Society. New Series 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 Israel Journal of Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Mathematical Physics 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 the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 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 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 Chebyshevskiĭ Sbornik 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Topology 1 Quantum Topology 1 Axioms 1 Journal of Applied and Computational Topology 1 Peking Mathematical Journal all top 5 Cited in 24 Fields 307 Manifolds and cell complexes (57-XX) 15 Combinatorics (05-XX) 10 Computer science (68-XX) 8 Global analysis, analysis on manifolds (58-XX) 6 Group theory and generalizations (20-XX) 5 Convex and discrete geometry (52-XX) 5 Biology and other natural sciences (92-XX) 3 Algebraic topology (55-XX) 3 Quantum theory (81-XX) 2 History and biography (01-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-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 Operator theory (47-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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