AdS 3-manifolds and Higgs bundles
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- by Daniele Alessandrini and Qiongling Li PDF
- Proc. Amer. Math. Soc. 146 (2018), 845-860
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
- MR Author ID: 849772
- 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
- MR Author ID: 1149454
- Email: qiongling.li@gmail.com
- 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
- © Copyright 2017 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
- MathSciNet review: 3731716