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Homotopy L-infinity spaces and Kuranishi manifolds, I: categorical structures

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arxiv 1602.00150 v1 pith:65PHEHEJ submitted 2016-01-30 math.DG math.AGmath.SG

Junwu Tu This is my paper · ORCID
classification math.DGmath.AGmath.SG
keywords kuranishimanifoldsspacestheoryhomotopytypecategorygauge
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abstract

Motivated by the definition of homotopy $L_\infty$ spaces, we develop a new theory of Kuranishi manifolds, closely related to Joyce's recent theory. We prove that Kuranishi manifolds form a $2$-category with invertible $2$-morphisms, and that certain fiber product property holds in this $2$-category. In a subsequent paper, we construct the virtual fundamental cycle of a compact oriented Kuranishi manifold, and prove some of its basic properties. Manifest from this new formulation is the fact that $[0,1]$-type homotopy $L_\infty$ spaces are naturally Kuranishi manifolds. The former structured spaces naturally appear as derived enhancements of Maurer-Cartan moduli spaces from Chern-Simons type gauge theory. In this way, Kuranishi manifolds theory can be applied to study path integrals in such type of gauge theories.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Kuranishi chart categories and higher cocycle conditions

    math.SG 2026-07 unverdicted novelty 7.0 of 10

    Kuranishi chart categories satisfy a higher homotopical bundle-component cocycle condition automatically, replacing rigid conditions with flexible homotopy-theoretic compatibility.

  2. $L_{\infty}$-Kuranishi spaces and the moduli space of pseudoholomorphic disks

    math.SG 2025-11 conditional novelty 6.0 of 10

    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.

  3. Categorical structures of Kuranishi spaces with $L_{\infty}[1]$-algebras

    math.SG 2026-07 unverdicted novelty 5.0 of 10

    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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