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AdS 3-manifolds and Higgs bundles


Authors: Daniele Alessandrini and Qiongling Li
Journal: Proc. Amer. Math. Soc. 146 (2018), 845-860
MSC (2010): Primary 57M20, 53C07; Secondary 58E12, 58E20
DOI: https://doi.org/10.1090/proc/13586
Published electronically: October 23, 2017
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Abstract: In this paper we investigate the relationships between closed AdS $ 3$-manifolds and Higgs bundles. We have a new way to construct AdS structures that allows us to see many of their properties explicitly, for example we can recover the very recent formula by Tholozan for their volume.

We give natural foliations of the AdS structure with time-like geodesic circles and we use these circles to construct equivariant minimal immersions of the Poincaré disc into the Grassmannian of time-like 2-planes of $ \mathbb{R}^{2,2}$.


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Additional Information

Daniele Alessandrini
Affiliation: Mathematisches Institut, Universitaet Heidelberg, INF 205, 69120, Heidelberg, Germany
Email: daniele.alessandrini@gmail.com

Qiongling Li
Affiliation: Centre for Quantum Geometry of Moduli Spaces (QGM), Aarhus University, Ny Munkegade 118, 8000 Aarhus C, Denmark – and – Department of Mathematics, California Institute of Technology, 1200 East California Boulevard, Pasadena, California 91125
Email: qiongling.li@gmail.com

DOI: https://doi.org/10.1090/proc/13586
Received by editor(s): October 28, 2015
Received by editor(s) in revised form: November 9, 2015, September 25, 2016, and November 14, 2016
Published electronically: October 23, 2017
Additional Notes: This work was started when both authors were visiting MSRI. Research at MSRI was supported in part by NSF grant DMS-0441170. 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). The second author was supported by the center of excellence grant ‘Center for Quantum Geometry of Moduli Spaces’ from the Danish National Research Foundation (DNRF95).
Communicated by: Michael Wolf
Article copyright: © Copyright 2017 Daniele Alessandrini and Qiongling Li

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