Dr. Abigail Thompson

Biography

Professor Abigail Thompson studies combinatorial methods in 3-dimensional topology. Her recent work emphasizes algebraic geometric techniques, quantum groups, hyperbolic geometry, and algebraic varieties related to the study of 3-manifolds. Notably, she has collaborated with M. Scharlemann to obtain new classification results and proofs concerning 3-manifolds using important concepts like thin position. Thompson's research has implications for understanding the primitive descriptions of 3-manifolds and the algorithms that can decide their homeomorphism types, including contributions toward the progress of the Poincaré conjecture. For instance, her work on band-connected sums of knots provides good evidence for knots satisfying Property P, which could lead to significant advancements in the theory surrounding this conjecture. She has published multiple significant papers in renowned journals regarding knots, Heegaard splittings, and recognition problems in topology.

Research Interests