AdS 3-manifolds and Higgs bundles

Creators: Alessandrini, Daniele; Li, Qiongling

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 ℝ^(2,2).

Additional Information

© 2017 Daniele Alessandrini and Qiongling Li. Received by the editors October 28, 2015 and, in revised form, November 9, 2015, September 25, 2016 and November 14, 2016. 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). We wish to thank many people for useful conversations and comments about this topic. In particular we thank Brian Collier, Bill Goldman, Fanny Kassel, Nicolas Tholozan, Anna Wienhard and Mike Wolf. We also thank the anonymous referee for many useful comments and suggestions.

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