Khovanov homology can distinguish exotic Mazur manifolds

Abstract

In a recent breakthrough, Ren and Willis gave the first analysis-free proof of the existence of exotic compact, orientable 4-manifolds; their main tool is the Khovanov skein lasagna module defined by Morrison, Walker, and Wedrich. In this paper, we introduce a new, simple way of using Khovanov homology to distinguish certain exotic compact, orientable 4-manifolds; our new method does not depend on the skein lasagna module. As an application, we give the first analysis-free proof of the existence of exotic Mazur manifolds, i.e. compact, contractible 4-manifolds that have handle decompositions with a single 1-handle and a single 2-handle.