Asymptotics of Higgs bundles in the Hitchin component
- Creators
- Collier, Brian
- Li, Qiongling
Abstract
In this paper we pursue a more geometric approach to compactification of the Hitchin component. Our main motivation is Wolf's harmonic map interpretation of Thurston's compactification of Teichmüller space with measured foliations. Using Hitchin's parameterization of the Hitchin component by holomorphic differentials, we study asymptotics of certain rays of representations. More precisely, along these rays we solve the Hitchin equations asymptotically and use the solution to study the asymptotics of the parallel transport operator of the associated flat connection. The asymptotics of the corresponding family of equivariant harmonic maps to the symmetric space SL(n,R)/SO(n,R) proves a conjecture of Katzarkov, Noll, Pandit and Simpson [17] on the Hitchin WKB problem in our setting.
Additional Information
© 2016 Elsevier Inc. Received 13 July 2015, Revised 10 November 2016, Accepted 21 November 2016, Available online 28 November 2016. The authors would like to thank their advisors Steve Bradlow and Mike Wolf for encouraging this collaboration and for their instructive comments. We also thank John Loftin and Jakob Blaavand for their many helpful comments, and Andy Sanders and Daniele Alessandrini for numerous enlightening conversations. We also graciously thank the referee for many useful comments and corrections. Both authors acknowledge the support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 "RNMS: GEometric structures And Representation varieties" (the GEAR Network). Our collaboration would not have been possible without this support. The second author is supported by the center of excellence grant 'Center for Quantum Geometry of Moduli Spaces' from the Danish National Research Foundation (DNRF95).Attached Files
Submitted - 1405.1106.pdf
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Additional details
- Eprint ID
- 78840
- DOI
- 10.1016/j.aim.2016.11.031
- Resolver ID
- CaltechAUTHORS:20170707-095300017
- NSF
- DMS-1107452
- NSF
- DMS-1107263
- NSF
- DMS-1107367
- Danish National Research Foundation
- DNRF95
- Created
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2017-07-07Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field