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Homotopy L-infinity spaces
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In this paper, we introduce a new class of structured spaces which is locally modeled by Costello's L-infinity spaces. This provides an alternative approach to study the derived geometric structures in the algebraic, analytic, or smooth category. Our main result asserts that on a compact complex manifold, the moduli space of simple holomorphic structures on a complex vector bundle with a fixed determinant bundle, admits a natural analytic homotopy L-infinity enhancement.
Forward citations
Cited by 3 Pith papers
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Kuranishi chart categories and higher cocycle conditions
Kuranishi chart categories satisfy a higher homotopical bundle-component cocycle condition automatically, replacing rigid conditions with flexible homotopy-theoretic compatibility.
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$L_{\infty}$-Kuranishi spaces and the moduli space of pseudoholomorphic disks
The moduli space of pseudoholomorphic disks is given a new 'L∞-Kuranishi space' structure — but only under an unproved Whitney-stratification/tubular-neighborhood assumption on each chart.
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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.
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