USC Topology Seminar: Exotic R4's with Compactly Supported Diffeomorphisms

Abhishek Shivkumar, University of Texas, Austin

Title: Exotic R^4's with Compactly Supported Diffeomorphisms

Abstract: A diffeomorphism is exotic if it is topologically but not smoothly isotopic to the identity. We show that for diffeomorphisms of closed simply-connected 4-manifolds dissolving under a single stabilization, there is a natural induced diffeomorphism on an exotic copy of R^4. We thereby construct exotic copies of R^4 with nontrivial compactly supported mapping class groups of arbitrarily large rank. This follows from a modified construction of corks for exotic diffeomorphisms due to Krushkal-Mukherjee-Powell-Warren. Time permitting, we will show how these examples can be extended to uncountable families thereof by end-summing with a particular exotic R^4.