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

Publication date: 17 May 2022

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

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Moduli problems for differential geometric structures (58D27) Moduli problems for topological structures (58D29) Applications of global analysis to structures on manifolds (57R57) Families, moduli, classification: algebraic theory (14J10) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) Deformations of singularities (14B07) Compactification of analytic spaces (32J05) Topological groups, Lie groups (22-XX) Invariants of 4-manifolds (including Donaldson and Seiberg-Witten invariants) (57K41)

This page was built for publication: Fredholm topology and enumerative geometry: reflections on some words of Michael Atiyah

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6399429)