ALERT: This system is being upgraded on Tuesday December 12. It will not be available
for use for several hours that day while the upgrade is in progress. Deposits to DukeSpace
will be disabled on Monday December 11, so no new items are to be added to the repository
while the upgrade is in progress. Everything should be back to normal by the end of
day, December 12.
Hodge Theory of the Turaev Cobracket and the Kashiwara--Vergne Problem
Abstract
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 an algebraic framing is a
morphism of mixed Hodge structure. We combine this with results of a previous
paper (arXiv:1710.06053) on the Goldman bracket to construct torsors of
solutions of 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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/24131Published Version (Please cite this version)
10.4171/JEMS/1088Publication Info
(2021). Hodge Theory of the Turaev Cobracket and the Kashiwara--Vergne Problem. Journal of the European Mathematical Society, 23(12). pp. 3889-3933. 10.4171/JEMS/1088. Retrieved from https://hdl.handle.net/10161/24131.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
Collections
More Info
Show full item recordScholars@Duke
Richard Hain
Professor of Mathematics
I am a topologist whose main interests include the study of the topology of complex
algebraic varieties (i.e. spaces that are the set of common zeros of a finite number
of complex polynomials). What fascinates me is the interaction between the topology,
geometry and arithmetic of varieties defined over subfields of the complex numbers,
particularly those defined over number fields. My main tools include differential
forms, Hodge theory and Galois theory, in addition to the more traditional to
Articles written by Duke faculty are made available through the campus open access policy. For more information see: Duke Open Access Policy
Rights for Collection: Scholarly Articles
Works are deposited here by their authors, and represent their research and opinions, not that of Duke University. Some materials and descriptions may include offensive content. More info