Fredholm topology and enumerative geometry: reflections on some words of Michael Atiyah

Abstract

The first part of this article is a short and selective survey of developments in differential and algebraic geometry from the 1980's involving enumerative questions and nonlinear elliptic partial differential equations. In the second part we discuss possible extensions of these ideas to structures on 4-manifolds, in particular to complex structures on surfaces of general type

Published in Proceedings of the Gokova Geometry-Topology Conference 2018/19. Special Issue in memory of Michael Atiyah