Hypercommutative Operad as a Homotopy Quotient of BV

A. Khoroshkin, N. Markarian, S. Shadrin

Research output: Contribution to journalArticlepeer-review


We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/Δ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other words we derive an equivalence of Hycomm-algebras and BV-algebras enhanced with a homotopy that trivializes the BV-operator. These formulas are given in terms of the Givental graphs, and are proved in two different ways. One proof uses the Givental group action, and the other proof goes through a chain of explicit formulas on resolutions of Hycomm and BV. The second approach gives, in particular, a homological explanation of the Givental group action on Hycomm-algebras.

Original languageAmerican English
Pages (from-to)697-729
Number of pages33
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - Sep 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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