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arXiv · 1508.01844

The topology of Kuranishi atlases

Dusa McDuff·Katrin Wehrheim
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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.

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Dusa McDuff, Katrin Wehrheim. 2015-08-08. The topology of Kuranishi atlases. https://doi.org/10.1112/plms.12032

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