The topology of Kuranishi atlases

Abstract

Kuranishi structures were introduced in the 1990s by Fukaya and Ono for the purpose of assigning a virtual cycle to moduli spaces of pseudoholomorphic curves that cannot be regularized by geometric methods. Starting from the same core idea (patching local finite dimensional reductions) we develop a theory of topological Kuranishi atlases and cobordisms that transparently resolves algebraic and topological challenges in this virtual regularization approach. It applies to any Kuranishi-type setting, e.g. atlases with isotropy, boundary and corners, or lack of differentiable structure.

replaces parts of arXiv:1208.1340; v2 adjusts some cross-references

References in corpus (3)

• Kuranishi homology and Kuranishi cohomology
• The polyfold--Kuranishi correspondence I: A choice-independent theory of Kuranishi structures
• Genus zero Gromov-Witten axioms via Kuranishi atlases

Cited by in corpus (3)

• Contact homology and virtual fundamental cycles
• Holomorphic curves in exploded manifolds: virtual fundamental class
• Constructing the virtual fundamental class of a Kuranishi atlas