Date/Time
Date(s) - 25/11/2024
3:30 pm - 4:30 pm

Location: Hamilton Hall, Room 302

Speaker: Geunyoung Kim

Title: High-dimensional contractible manifolds

Abstract: In 1961, Mazur constructed a contractible, compact, smooth 4-manifold which is not homeomorphic to the standard 4-ball, using a 0-handle, a 1-handle and a 2-handle.  In this talk, for any integer n ? 2, we construct a contractible, compact, smooth (n+3)-manifold which is not homeomorphic to the standard (n+3)-ball, using a 0-handle, an n-handle and an (n+1)-handle. The key step is the construction of an interesting knotted n-sphere in Sn × S2 generalizing the Mazur pattern. As a corollary, for any integer n ? 2, there exists a smooth involution of Sn+3 whose fixed point set is a non-simply connected homology (n + 2)-sphere.