ADS 3-manifolds and Higgs bundles

Daniele Alessandrini; Qiongling Li

doi:10.1090/proc/13586

ADS 3-manifolds and Higgs bundles

Daniele Alessandrini
, Qiongling Li

Department of Mathematical Sciences

Aarhus University
California Institute of Technology

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	845-860
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	2
DOIs	https://doi.org/10.1090/proc/13586
State	Published - 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 Poincar{\'e} disc into the Grassmannian of time-like 2-planes of R2,2.",

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AB - 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 R2,2.

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ADS 3-manifolds and Higgs bundles

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