Topology Seminar- "Contractible 4-manifolds and Knots in S^1xS^2."

Speaker:  Jack Calcut (Oberlin College)

Time: November 3 (Thursday), 2022; 4:45pm-6:00

Room:  TOMP 302

Title: "Contractible 4-manifolds and Knots in S^1xS^2."

Abstract: 

Mazur and Poénaru constructed the first compact, contractible manifolds distinct from disks. More recently, Sparks modified Mazur's construction and defined Jester manifolds. Sparks used Jester manifolds to produce compact, contractible 4-manifolds distinct from the 4-disk that split as the union of two 4-disks meeting in a 4-disk. We survey several very different proofs that all Mazur and Jester manifolds are not 4-disks. We discuss the problem of distinguishing these 4-manifolds from one another. And, we present pertinent questions on knots in S^1xS^2 and hyperbolic triangle groups. This is joint work with Alexandra Du.