On the bv structure on the cohomology of moduli space

Sümeyra Sakallı, Alexander A. Voronov

Research output: Contribution to journalArticlepeer-review

Abstract

The question of vanishing of the BV operator on the cohomology of the moduli space of Riemann surfaces is investigated. The BV structure, which comprises a BV operator and an antibracket, is identified, vanishing theorems are proven, and a counterexample is provided.

Original languageEnglish (US)
Pages (from-to)755-773
Number of pages19
JournalPure and Applied Mathematics Quarterly
Volume16
Issue number3
DOIs
StatePublished - 2020

Bibliographical note

Funding Information:
With admiration and gratitude, we dedicate this paper to Kyoji Saito. The breadth of his interests touched upon the topics of this paper as well: his recent paper [26] uses the BV-algebra of multivector fields on a Calabi-Yau manifold, whereas his interest in the moduli spaces is long-standing, see [35, 36, 37, 38]. We are grateful to Weiyan Chen, Domenico D?Alessandro, S?ren Galatius, and Craig Westerland for useful discussions. SS also thanks the Max Planck Institute for Mathematics, Bonn, for its great research environment and support. AV was supported by the World Premier International Research Center Initiative (WPI), MEXT, Japan, and a Collaboration grant from the Simons Foundation (#585720).

Funding Information:
36, 37, 38]. We are grateful to Weiyan Chen, Domenico D’Alessandro, Søren Galatius, and Craig Westerland for useful discussions. SS also thanks the Max Planck Institute for Mathematics, Bonn, for its great research environment and support. AV was supported by the World Premier International Research Center Initiative (WPI), MEXT, Japan, and a Collaboration grant from the Simons Foundation (#585720).

Keywords

  • BV-algebra
  • Deligne-Mumford compactification
  • Maurer-Cartan equation
  • Mixed Hodge structure
  • Moduli space of Riemann surfaces
  • Quantum master equation
  • Spectral sequence
  • Stable cohomology
  • Tautological class

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