Joint GT-UGA Seminar at GT - Simply-connected, spineless 4-manifolds

Series: 
Geometry Topology Seminar
Monday, April 22, 2019 - 2:00pm
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Duke University
Organizer: 

Given an m-dimensional manifold M that is homotopy equivalent to an n-dimensional manifold N (where n<m), a spine of M is a piecewise-linear embedding of N into M (not necessarily locally flat) realizing the homotopy equivalence. When m-n=2 and m>4, Cappell and Shaneson showed that if M is simply-connected or if m is odd, then it contains a spine. In contrast, I will show that there exist smooth, compact, simply-connected 4-manifolds which are homotopy equivalent to the 2-sphere but do not contain a spine (joint work with Tye Lidman). I will also discuss some related results about PL concordance of knots in homology spheres (joint with Lidman and Jen Hom).