Department of Mathematics - Master Calendar

Abstract: Examples of exotic 4-manifolds, which are homeomorphic but not diffeomorphic, are plentiful, but not well understood. Most examples are constructed via modification: some kind of surgery is done on an embedded surface where, one hopes and prays that the topological structure is preserved, but some smooth invariant is changed. This talk will discuss examples of exotic 4-manifolds that are aspherical, and the peculiarities involved in constructing them and detecting that they are exotic. These 4-manifolds provide a counterexample to the smooth Borel conjecture in dimension 4, which states that a homotopy equivalence between 4-manifolds should be homotopic to a diffeomorphism. This is joint work with Mike Davis, Kyle Hayden, Jingyin Huang, and Danny Ruberman.