TY - JOUR
T1 - Higgs bundles and geometric structures on manifolds
AU - Alessandrini, Daniele
N1 - Publisher Copyright:
© 2019, Institute of Mathematics. All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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 at bundles. Higgs bundles can be very useful in describing at 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.
AB - 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 at bundles. Higgs bundles can be very useful in describing at 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.
KW - Anosov representations
KW - Geometric structures
KW - Higgs bundles
KW - Higher teichmüller theory
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U2 - 10.3842/SIGMA.2019.039
DO - 10.3842/SIGMA.2019.039
M3 - Article
AN - SCOPUS:85068662909
VL - 15
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
M1 - 039
ER -