Hodge theory of the Goldman bracket

Hain, Richard

doi:10.2140/gt.2020.24.1841

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Hodge theory of the Goldman bracket

Richard Hain

Geometry & Topology 24 (2020) 1841–1906

DOI: 10.2140/gt.2020.24.1841

Abstract

We show that, after completing in the $I$ –adic topology, the Goldman bracket on the space spanned by the closed geodesics on a smooth, complex algebraic curve $X$ is a morphism of mixed Hodge structures. We prove similar statements for the natural action of the loops in $X$ on paths from one boundary vector to another.

Dedicated to the memory of Stefan Papadima

Keywords

Goldman bracket, Hodge theory

Mathematical Subject Classification 2010

Primary: 17B62, 58A12

Secondary: 57N05, 14C30

References

Publication

Received: 8 January 2019

Revised: 8 October 2019

Accepted: 26 November 2019

Published: 10 November 2020

Proposed: Dan Abramovich

Seconded: Ulrike Tillmann, Frances Kirwan

Authors

Richard Hain
Department of Mathematics Duke University Durham, NC United States

Volume 24, issue 4 (2020)