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