Hodge theory of the Turaev cobracket and the Kashiwara-Vergne problem

Journal Article (Journal Article)

In this paper we show that, after completing in the I -adic topology, the Turaev cobracket on the vector space freely generated by the closed geodesics on a smooth, complex algebraic curve X with a quasi-algebraic framing is a morphism of mixed Hodge structure. We combine this with results of a previous paper on the Goldman bracket to construct torsors of solutions to the Kashiwara-Vergne problem in all genera. The solutions so constructed form a torsor under a prounipotent group that depends only on the topology of the framed surface. We give a partial presentation of these groups. Along the way, we give a homological description of the Turaev cobracket.

Full Text

Duke Authors

Cited Authors

  • Hain, R

Published Date

  • January 1, 2021

Published In

Volume / Issue

  • 23 / 12

Start / End Page

  • 3889 - 3933

International Standard Serial Number (ISSN)

  • 1435-9855

Digital Object Identifier (DOI)

  • 10.4171/JEMS/1088

Citation Source

  • Scopus