Higgs Bundles and Geometric Structures on Manifolds

Abstract:

Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people and they play an important role in higher Teichmüller theory. Geometric structures on a manifold are closely related with representations of the fundamental group and with flat bundles. Higgs bundles can be very useful in describing flat bundles explicitly, via solutions of Hitchin’s equations. Baraglia has shown in his Ph.D. Thesis that Higgs bundles can also be used to construct geometric structures in some interesting cases. In this paper, we will explain the main ideas behind this theory and we will survey some recent results in this direction, which are joint work with Qiongling Li.

SEEK ID: https://publications.h-its.org/publications/978

DOI: 10.3842/SIGMA.2019.039

Research Groups: Groups and Geometry

Publication type: Journal

Journal: Symmetry, Integrability and Geometry: Methods and Applications

Publisher: SIGMA (Symmetry, Integrability and Geometry: Methods and Application)

Citation: SIGMA 15 039:32

Date Published: 10th May 2019

URL: https://www.emis.de/journals/SIGMA/2019/039/

Registered Mode: imported from a bibtex file

Author: Daniele Alessandrini

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Citation
Alessandrini, D., & . (2019). Higgs Bundles and Geometric Structures on Manifolds. In Symmetry, Integrability and Geometry: Methods and Applications. SIGMA (Symmetry, Integrability and Geometry: Methods and Application). https://doi.org/10.3842/sigma.2019.039
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Created: 30th Jan 2020 at 09:59

Last updated: 5th Mar 2024 at 21:24

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