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A geometric construction of the Witten genus, II

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arxiv 1112.0816 v2 pith:VIIMDXWA submitted 2011-12-05 math.QA math.AT

Kevin J. Costello This is my paper · ORCID
classification math.QAmath.AT
keywords constructiongenustheorywittenannouncedarxivcompactcomplex
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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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Cited by 2 Pith papers

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

  1. $L_{\infty}$-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.

  2. 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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