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## Thompson, Abigail A.

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 Author ID: thompson.abigail-a Published as: Thompson, Abigail; Thompson, Abigail A.; Thompson, A. Homepage: https://www.math.ucdavis.edu/~thompson/ External Links: Women in Mathematics · MGP · Wikidata · MacTutor
 Documents Indexed: 37 Publications since 1987
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#### Co-Authors

 12 single-authored 15 Scharlemann, Martin G. 6 Hass, Joel 2 Rubinstein, J. Hyam 2 Tsvietkova, Anastasiia 1 Goda, Hiroshi 1 Gompf, Robert E. 1 Johnson, Jesse Edward 1 Kirby, Robion Cromwell 1 Menasco, William W. 1 Thurston, William Paul
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#### Serials

 5 Topology 3 Proceedings of the American Mathematical Society 3 Journal of Knot Theory and its Ramifications 3 Geometry & Topology 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 Illinois Journal of Mathematics 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 Mathematical Research Letters
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#### Fields

 35 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)

#### Citations contained in zbMATH Open

32 Publications have been cited 386 times in 285 Documents Cited by Year
Thin position for 3-manifolds. Zbl 0818.57013
Scharlemann, Martin; Thompson, Abigail
1994
Thin position and the recognition problem for $$S^ 3$$. Zbl 0849.57009
Thompson, Abigail
1994
Heegaard splittings of $$(\text{surface})\times I$$ are standard. Zbl 0814.57010
Scharlemann, Martin; Thompson, Abigail
1993
Link genus and the Conway moves. Zbl 0693.57004
Scharlemann, Martin; Thompson, Abigail
1989
Thin position and bridge number for knots in the 3-sphere. Zbl 0867.57009
Thompson, Abigail
1997
Unknotting number, genus and companion tori. Zbl 0616.57003
Scharlemann, Martin; Thompson, Abigail
1988
Thin position and Heegaard splittings of the 3-sphere. Zbl 0820.57005
Scharlemann, Martin; Thompson, Abigail
1994
The disjoint curve property and genus 2 manifolds. Zbl 0935.57022
Thompson, Abigail
1999
Finding disjoint Seifert surfaces. Zbl 0654.57005
Scharlemann, Martin; Thompson, Abigail
1988
Levelling an unknotting tunnel. Zbl 0958.57007
Goda, Hiroshi; Scharlemann, Martin; Thompson, Abigail
2000
Stabilization of Heegaard splittings. Zbl 1177.57018
Hass, Joel; Thompson, Abigail; Thurston, William
2009
Unknotting tunnels and Seifert surfaces. Zbl 1047.57008
Scharlemann, Martin; Thompson, Abigail
2003
Detecting unknotted graphs in 3-space. Zbl 0751.05033
Scharlemann, Martin; Thompson, Abigail
1991
On tunnel number one knots that are not $$(1, n)$$. Zbl 1218.57008
Johnson, Jesse; Thompson, Abigail
2011
Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures. Zbl 1214.57008
Gompf, Robert E.; Scharlemann, Martin; Thompson, Abigail
2010
Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds. Zbl 1071.57015
Scharlemann, Martin; Thompson, Abigail
2005
Knots with unknotting number one are determined by their complements. Zbl 0677.57006
Thompson, Abigail
1989
On the additivity of knot width. Zbl 1207.57016
Scharlemann, Martin; Thompson, Abigail
2004
Surgery on a knot in (surface $$\times I$$). Zbl 1197.57011
Scharlemann, Martin; Thompson, Abigail A.
2009
Property P for the band-connect sum of two knots. Zbl 0628.57005
Thompson, Abigail
1987
Algorithmic recognition of 3-manifolds. Zbl 0890.57027
Thompson, Abigail
1998
A polynomial invariant of graphs in 3-manifolds. Zbl 0773.57002
Thompson, Abigail
1992
Thinning genus two Heegaard spines in $$S^ 3$$. Zbl 1048.57002
Scharlemann, Martin; Thompson, Abigail
2003
Compressing handlebodies with holes. Zbl 0683.57004
Menasco, W.; Thompson, A.
1989
Thurston norm minimizing surfaces and skein trees for links in $$S^ 3$$. Zbl 0686.57004
Thompson, Abigail
1989
A necessary and sufficient condition for a 3-manifold to have Heegaard genus one. Zbl 0694.57006
Hass, Joel; Thompson, Abigail
1989
A new invariant of 4-manifolds. Zbl 1421.57031
Kirby, Robion; Thompson, Abigail
2018
The number of surfaces of fixed genus in an alternating link complement. Zbl 1405.57014
Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia
2017
Neon bulbs and the unknotting of arcs in manifolds. Zbl 0886.57003
Hass, Joel; Thompson, Abigail
1997
Invariants of curves in $$\mathbb RP^2$$ and $$\mathbb R^2$$. Zbl 1128.53010
Thompson, Abigail
2006
Knots and $$k$$-width. Zbl 1189.57005
Hass, Joel; Rubinstein, J. Hyam; Thompson, Abigail
2009
3-manifolds with Heegaard splittings of distance two. Zbl 1282.57026
Rubinstein, J. Hyam; Thompson, Abigail
2013
A new invariant of 4-manifolds. Zbl 1421.57031
Kirby, Robion; Thompson, Abigail
2018
The number of surfaces of fixed genus in an alternating link complement. Zbl 1405.57014
Hass, Joel; Thompson, Abigail; Tsvietkova, Anastasiia
2017
3-manifolds with Heegaard splittings of distance two. Zbl 1282.57026
Rubinstein, J. Hyam; Thompson, Abigail
2013
On tunnel number one knots that are not $$(1, n)$$. Zbl 1218.57008
Johnson, Jesse; Thompson, Abigail
2011
Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures. Zbl 1214.57008
Gompf, Robert E.; Scharlemann, Martin; Thompson, Abigail
2010
Stabilization of Heegaard splittings. Zbl 1177.57018
Hass, Joel; Thompson, Abigail; Thurston, William
2009
Surgery on a knot in (surface $$\times I$$). Zbl 1197.57011
Scharlemann, Martin; Thompson, Abigail A.
2009
Knots and $$k$$-width. Zbl 1189.57005
Hass, Joel; Rubinstein, J. Hyam; Thompson, Abigail
2009
Invariants of curves in $$\mathbb RP^2$$ and $$\mathbb R^2$$. Zbl 1128.53010
Thompson, Abigail
2006
Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds. Zbl 1071.57015
Scharlemann, Martin; Thompson, Abigail
2005
On the additivity of knot width. Zbl 1207.57016
Scharlemann, Martin; Thompson, Abigail
2004
Unknotting tunnels and Seifert surfaces. Zbl 1047.57008
Scharlemann, Martin; Thompson, Abigail
2003
Thinning genus two Heegaard spines in $$S^ 3$$. Zbl 1048.57002
Scharlemann, Martin; Thompson, Abigail
2003
Levelling an unknotting tunnel. Zbl 0958.57007
Goda, Hiroshi; Scharlemann, Martin; Thompson, Abigail
2000
The disjoint curve property and genus 2 manifolds. Zbl 0935.57022
Thompson, Abigail
1999
Algorithmic recognition of 3-manifolds. Zbl 0890.57027
Thompson, Abigail
1998
Thin position and bridge number for knots in the 3-sphere. Zbl 0867.57009
Thompson, Abigail
1997
Neon bulbs and the unknotting of arcs in manifolds. Zbl 0886.57003
Hass, Joel; Thompson, Abigail
1997
Thin position for 3-manifolds. Zbl 0818.57013
Scharlemann, Martin; Thompson, Abigail
1994
Thin position and the recognition problem for $$S^ 3$$. Zbl 0849.57009
Thompson, Abigail
1994
Thin position and Heegaard splittings of the 3-sphere. Zbl 0820.57005
Scharlemann, Martin; Thompson, Abigail
1994
Heegaard splittings of $$(\text{surface})\times I$$ are standard. Zbl 0814.57010
Scharlemann, Martin; Thompson, Abigail
1993
A polynomial invariant of graphs in 3-manifolds. Zbl 0773.57002
Thompson, Abigail
1992
Detecting unknotted graphs in 3-space. Zbl 0751.05033
Scharlemann, Martin; Thompson, Abigail
1991
Link genus and the Conway moves. Zbl 0693.57004
Scharlemann, Martin; Thompson, Abigail
1989
Knots with unknotting number one are determined by their complements. Zbl 0677.57006
Thompson, Abigail
1989
Compressing handlebodies with holes. Zbl 0683.57004
Menasco, W.; Thompson, A.
1989
Thurston norm minimizing surfaces and skein trees for links in $$S^ 3$$. Zbl 0686.57004
Thompson, Abigail
1989
A necessary and sufficient condition for a 3-manifold to have Heegaard genus one. Zbl 0694.57006
Hass, Joel; Thompson, Abigail
1989
Unknotting number, genus and companion tori. Zbl 0616.57003
Scharlemann, Martin; Thompson, Abigail
1988
Finding disjoint Seifert surfaces. Zbl 0654.57005
Scharlemann, Martin; Thompson, Abigail
1988
Property P for the band-connect sum of two knots. Zbl 0628.57005
Thompson, Abigail
1987
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#### Cited by 241 Authors

 20 Scharlemann, Martin G. 13 Tomova, Maggy 11 Lei, Fengchun 9 Bachman, David 9 Kobayashi, Tsuyoshi 9 Qiu, Ruifeng 9 Schultens, Jennifer 9 Taylor, Scott A. 9 Thompson, Abigail A. 8 Li, Tao 7 Lee, Junghoon 7 Ozawa, Makoto 7 Sedgwick, Eric 7 Yang, Guoqiu 6 Cho, Sangbum 6 Johnson, Jesse Edward 6 Lackenby, Marc 6 Moriah, Yoav 6 Zou, Yanqing 5 Blair, Ryan C. 5 Burton, Benjamin A. 5 Du, Kun 5 Rubinstein, J. Hyam 5 Zupan, Alexander 4 Goda, Hiroshi 4 Kalfagianni, Efstratia 4 Li, Fengling 4 Luecke, John 4 McCullough, Darryl 4 Schleimer, Saul 4 Shimokawa, Koya 3 Bleiler, Steven A. 3 Derby-Talbot, Ryan 3 Gompf, Robert E. 3 Gordon, Cameron McA. 3 Guo, Qilong 3 Hass, Joel 3 Hayashi, Chuichiro 3 Ishihara, Kai 3 Jaco, William H. 3 Jang, Yeonhee 3 Kang, Ensil 3 Kim, Jungsoo 3 Koda, Yuya 3 Moore, Allison H. 3 Motegi, Kimihiko 3 Rieck, Yo’av 3 Takao, Kazuto 3 Taniyama, Kouki 3 Vazquez, Mariel 2 Agol, Ian 2 Baker, Kenneth L. 2 Balm, Cheryl Jaeger 2 Benedetti, Riccardo 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 Ivanov, Sergei Vladimirovich 2 Jang, Hee Jeong 2 Lee, Sang Youl 2 Lee, Sangjin 2 Li, Yang 2 Lidman, Tye 2 Lin, Xiao-Song 2 Lutz, Frank Hagen 2 Mangum, Brian S. 2 Manturov, Vassiliĭ Olegovich 2 Matsuda, Hiroshi 2 Meier, Jeffrey 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 Wagner, Uli 2 Wilson, Robin Todd 1 Appleboim, Eli 1 Armas-Sanabria, Lorena 1 Askitas, Nikos 1 Bart, Anneke 1 Barthel, Senja 1 Berge, John 1 Birman, Joan S. 1 Björner, Anders 1 Bobtcheva, Ivelina 1 Borodzik, Maciej 1 Bryant, Birch 1 Buck, Dorothy 1 Bullock, Doug 1 Campisi, Marion Moore ...and 141 more Authors
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#### Cited in 58 Serials

 45 Algebraic & Geometric Topology 44 Topology and its Applications 35 Journal of Knot Theory and its Ramifications 23 Transactions of the American Mathematical Society 22 Geometry & Topology 19 Proceedings of the American Mathematical Society 10 Geometriae Dedicata 9 Mathematische Annalen 4 Mathematical Proceedings of the Cambridge Philosophical Society 3 Chaos, Solitons and Fractals 3 Advances in Mathematics 3 Inventiones Mathematicae 3 Osaka Journal of Mathematics 3 Chinese Annals of Mathematics. Series B 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Duke Mathematical Journal 2 Michigan Mathematical Journal 2 Tokyo Journal of Mathematics 2 Geometric and Functional Analysis. GAFA 2 Bulletin of the American Mathematical Society. New Series 2 Experimental Mathematics 2 Acta Mathematica Sinica. English Series 2 Science China. Mathematics 2 Journal of Singularities 2 Winter Braids Lecture Notes 1 Israel Journal of Mathematics 1 Journal of Mathematical Physics 1 Mathematics of Computation 1 Cahiers de Topologie et Géométrie Différentielle Catégoriques 1 Compositio Mathematica 1 Indiana University Mathematics Journal 1 Journal of Combinatorial Theory. Series A 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 Discrete & Computational Geometry 1 Journal of the American Mathematical Society 1 Forum Mathematicum 1 Sugaku Expositions 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 St. Petersburg Mathematical Journal 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 Chebyshevskiĭ Sbornik 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Topology 1 Quantum Topology 1 Axioms
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#### Cited in 24 Fields

 279 Manifolds and cell complexes (57-XX) 13 Combinatorics (05-XX) 10 Computer science (68-XX) 8 Global analysis, analysis on manifolds (58-XX) 6 Group theory and generalizations (20-XX) 5 Biology and other natural sciences (92-XX) 4 Convex and discrete geometry (52-XX) 3 Algebraic topology (55-XX) 3 Quantum theory (81-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-XX) 1 History and biography (01-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 Operator theory (47-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX)

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