Lagrangian boundary conditions for anti-self-dual instantons and the Atiyah{\rm --}Floer conjecture}

Abstract

The purpose of this survey is to explain an approach to the Atiyah--Floer conjecture via a new instanton Floer homology with Lagrangian boundary conditions. This is a joint project with Dietmar Salamon; see [14] for an earlier exposition. This paper also provides a rough guide to the analysis of anti-self-dual instantons with Lagrangian boundary conditions in [21, 22], which is the crucial ingredient of our approach.