Speaker: Daniel Hartman
University of Georgia
Will give a Topology Seminar entitled:
Pseudo-isotopies of simply connected 4-manifolds
Abstract: Published in 1986, Quinn provided a proof that, for simply connected 4-manifolds, any homeomorphism pseudoisotopic to the identity is actually isotopic to the identity. Additionally for smooth manifolds, diffeomorphisms that are pseudoisotopic are smoothly stably isotopic. Both of these results are fundamental to the world of 4-manifolds. Now part of the strategy Quinn's employs for deriving these results revolves around understanding and manipulating a specific collection of embedded disks. There is one particular "move" that is critical to Quinn's argument: the replacement criterion. However, the justification for using this move is incorrect. I plan to discuss the replacement criterion and give a way to circumvent it in order to complete Quinn's proofs.
Date: 02-27-2024
Time: 2:30 pm
Location: 258 Hurley Bldg