Abigail Thompson

Abigail A. Thompson (born June 30, 1958 in Norwalk , Connecticut ) is an American mathematician who deals with knot theory and the geometric topology of 3- manifolds .

Thompson attended Wellesley College (Bachelor's degree 1979) and Rutgers University , where she received her doctorate in 1986 with Martin Scharlemann ( Property P for some classes of knots ). As a post-doctoral student she was at Hebrew University with a Lady Davis Fellowship and at the University of California, Berkeley in 1987/88 . Since 1988 she has been a professor at the University of California, Davis . In 1990/91 and from 2000 to 2001 she was at the Institute for Advanced Study . She is also involved in math education and runs a regular summer school at her university for gifted high school students.

In her dissertation, she supported the conjecture that all non-trivial knots in three-dimensional Euclidean space have the property P (which means that no non-trivial stretching surgery of the knot complement yields the 3-sphere ) by using the property P for two showed more classes of knots.

She was a Sloan Research Fellow from 1991 to 1993 and is a Fellow of the American Mathematical Society . In 2003 she received the Ruth Lyttle Satter Prize in Mathematics in particular for work on expanding the concept of thin position in connection with the node invariant called "width" (introduced by David Gabai in 1987). With the help of this, she simplified (and gave a new interpretation for) one Algorithm by Hyam Rubinstein (1992) to decide when a closed orientable 3-manifold is homeomorphic to the 3-sphere.

She is married and has three children.

Fonts (selection)

with Scharlemann: Heegaard splittings of (surface) × I are standard. Math. Ann. 295 (1993) no. 3: 549-564.
Thin position and the recognition problem for S ³ . Math. Res. Lett. 1 (1994) no. 5, 613-630.

Web links

Homepage
Biography at Agnes Scott College
John J. O'Connor, Edmund F. Robertson : Abigail Thompson. In: MacTutor History of Mathematics archive .

Individual evidence

↑ Abigail Thompson in the Mathematics Genealogy Project (English)
↑ In the laudation, her work Thin position and the recognition problem for ${\ displaystyle S ^ {3}}$ , Math. Res. Letters, Volume 1, 1994, pp. 613–630, Thin position for 3-manifolds , Contemporary Mathematics Volume 164, 1994, p. 231 ( with Scharlemann), Thin position and Heegaard splittings of the 3-sphere , J. Differential Geom., Volume 39, 1994, pp. 343-357, Thin position and bridge number for knots in the 3-sphere , Topology, Volume 36, 1997, pp. 505-507, cited

personal data
SURNAME	Thompson, Abigail
ALTERNATIVE NAMES	Thompson, Abigail A.
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	June 30, 1958
PLACE OF BIRTH	Norwalk , Connecticut

[1] Abigail Thompson in the Mathematics Genealogy Project (English)

[2] In the laudation, her work Thin position and the recognition problem for ${\ displaystyle S ^ {3}}$ , Math. Res. Letters, Volume 1, 1994, pp. 613–630, Thin position for 3-manifolds , Contemporary Mathematics Volume 164, 1994, p. 231 ( with Scharlemann), Thin position and Heegaard splittings of the 3-sphere , J. Differential Geom., Volume 39, 1994, pp. 343-357, Thin position and bridge number for knots in the 3-sphere , Topology, Volume 36, 1997, pp. 505-507, cited