Volume 24, issue 4 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Hodge theory of the Goldman bracket

Richard Hain

Geometry & Topology 24 (2020) 1841–1906
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