Geometry and Topology Seminar – Charles Stine – Corks Equivalent to Fintushel-Stern Surgery
Oct 16, 2023
4:30PM to 5:30PM
Date(s) - 16/10/2023
4:30 pm - 5:30 pm
Title: Corks Equivalent to Fintushel-Stern Surgery
Abstract: Fintushel and Stern’s knot surgery constructions has been a central source of exotic 4-manifolds since its introduction in 1997. In the simply connected setting, it is known that there are also embedded corks in knot-surgered manifolds whose twists undo the knot surgery. This has been known abstractly since the construction was first given, but the explicit corks and embeddings have remained elusive. We will give an algorithmic process for transforming a generic Kirby diagram of a simply-connected knot surgered 4-manifold into one which contains an explicit cork whose twist undoes the surgery: answering the question. Along the way we will discuss $S^2 \times S^2$-stable diffeomorphisms of knot-surgered 4-manifolds, and their relationship to the existence of corks.