Defines L∞-Kuranishi spaces via L∞[1]-algebras on Kuranishi charts and proves they form a category embedding smooth manifolds, by modifying conditions from prior work.
A geometric construction of the Witten genus, II
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I give a rigorous construction of a 2-dimensional quantum field theory of maps from an elliptic curve to a compact complex manifold X, and I show that the partition function of this theory is the Witten genus of X. The results proved here were announced (in a slightly different form) in arXiv:1006.5422.
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Categorical structures of Kuranishi spaces with $L_{\infty}[1]$-algebras
Defines L∞-Kuranishi spaces via L∞[1]-algebras on Kuranishi charts and proves they form a category embedding smooth manifolds, by modifying conditions from prior work.