On the BV structure on the cohomology of moduli space

2019/12/30 by Sümeyra Sakallı, Sakallı, Sümeyra, Alexander A. Voronov +1
Mathematics · #14H15 (Primary) 14F17 #32G15 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic and Geometric Analysis #FOS: Mathematics #Geometric and Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1912.13045

openalex publication_date 2019/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Topological recursion relations in genus 2
• Homology of moduli spaces of curves and commutative homotopy algebras

Related

• Cohomology of moduli spaces
• Classes on the moduli space of Riemann surfaces through a noncommutative Batalin-Vilkovisky formalism
• The stable moduli space of Riemann surfaces: Mumford's conjecture
• Parabolic bundles and the intersection cohomology of moduli spaces of vector bundles on curves
• The cohomology of the moduli space of abelian varieties