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81 Publications visible to you, out of a total of 81
Representations and geometric structures

Abstract (Expand)

This note summarizes in an informal way some geometric properties of Anosov representations into the symplectic group, which were presented in a talk at the conference What is Next. The mathematical … legacy of Bill Thurston, held in June 2014 in Cornell.

Author: Anna Wienhard

Date Published: 2016

Publication Type: Misc

Basmajian-type inequalities for maximal representations

Abstract (Expand)

For suitable metrics on the locally symmetric space associated to a maximal representation, we prove inequalities between the length of the boundary and the lengths of orthogeodesics that generalize … the classical Basmajian’s identity from Teichmueller theory. Any equality characterizes diagonal embeddings.

Authors: Federica Fanoni, Maria Beatrice Pozzetti

Date Published: 2016

Publication Type: Misc

Holonomy map fibers of ℂP1-structures in moduli space

Abstract (Expand)

Let S be a closed oriented surface of genus g≥2. Fix an arbitrary non-elementary representation ρ\col\pi_1(S)\to \rm SL_2(\C) and consider all marked (complex) projective structures on S with holonomy …my ρ. We show that their underlying conformal structures are dense in the moduli space of S.

Authors: Shinpei Baba, Subhojoy Gupta

Date Published: 31st Aug 2015

Publication Type: Journal

Cameral data for SU(p+1,p)-Higgs bundles

Abstract (Expand)

We study the cameral and spectral data for the moduli space of polystable \SU(p+1,p)-Higgs bundles and deduce the latter from the former. As an application, we obtain that the Toledo invariant classifies … the connected components of the regular fibers of the Hitchin map.

Author: Ana Peón-Nieto

Date Published: 2015

Publication Type: Misc

Bounded cohomology via partial differential equations, I

Abstract (Expand)

We present a new technique that employs partial differential equations in order to explicitly construct primitives in the continuous bounded cohomology of Lie groups. As anapplication, we prove a … a vanishing theorem for the continuous bounded cohomology of SL(2,R) in degree four, establishing a special case of a conjecture of Monod.

Authors: Tobias Hartnick, Andreas Ott

Date Published: 2015

Publication Type: Journal

Compactification of certain Clifford-Klein forms of reductive homogeneous spaces

Abstract (Expand)

We describe smooth compactifications of certain families of reductive homogeneous spaces such as group manifolds for classical Lie groups, or pseudo-Riemannian analogues of real hyperbolic spaces and … their complex and quaternionic counterparts. We deduce compactifications of Clifford-Klein forms of these homogeneous spaces, namely quotients by discrete groups Gamma acting properly discontinuously, in the case that Gamma is word hyperbolic and acts via an Anosov representation. In particular, these Clifford-Klein forms are topologically tame.

Authors: François Guéritaud, Olivier Guichard, Fanny Kassel, Anna Wienhard

Date Published: 2015

Publication Type: Misc

ADS 3-manifolds and Higgs bundles

Abstract (Expand)

In this paper we investigate the relationships between closed \mathrmAdS 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 the volumes. We also find applications to the theory of minimal immersions into quadrics with their natural pseudo-Riemannian structure: using the geometry of the \mathrmAdS manifolds we can characterize the representations admitting equivariant minimal immersions of the Poincaré disc into the Klein quadric, the Grassmannian \mathrmGr(2,4), and understand the geometry of these minimal immersions.

Authors: Daniele Alessandrini, Qiongling Li

Date Published: 2015

Publication Type: Misc

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