Filter and export

Publications

What is a Publication?
62 Publications visible to you, out of a total of 62
Positivity and higher Teichmüller theory

Abstract (Expand)

We introduce Θ-positivity, a new notion of positivity in real semisimple Lie groups. The notion of Θ-positivity generalizes at the same time Lusztig’s total positivity in split real Lie groups as well … as well known concepts of positivity in Lie groups of Hermitian type. We show that there are two other families of Lie groups, \SO(p,q) for p<q, and a family of exceptional Lie groups, which admit a Θ-positive structure. We describe key aspects of Θ-positivity and make a connection with representations of surface groups and higher Teichmüller theory.

Authors: Olivier Guichard, Anna Wienhard

Date Published: 6th Aug 2018

Publication Type: InCollection

Schottky groups and maximal representations

Abstract (Expand)

We describe a construction of Schottky type subgroups of automorphism groups of partially cyclically ordered sets. We apply this construction to the Shilov boundary of a Hermitian symmetric space and … show that in this setting Schottky subgroups correspond to maximal representations of fundamental groups of surfaces with boundary. As an application, we construct explicit fundamental domains for the action of maximal representations into \mathrm Sp(2n,\mathbb R) on \mathbb RP^2n-1.

Authors: Jean-Philippe Burelle, Nicolaus Treib

Date Published: 1st Aug 2018

Publication Type: Journal

Simultaneous ips on triangulated surfaces

Abstract (Expand)

We investigate a type of distance between triangulations on finite-type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism, … and our main results are upper bounds on the distance between triangulations that only depend on the topology of the surface.

Authors: Valentina Disarlo, Hugo Parlier

Date Published: 1st Aug 2018

Publication Type: Journal

Higgs bundles for real groups and the Hitchin-Kostant-Rallis section

Abstract (Expand)

We consider the moduli space of polystable-twisted-Higgs bundles over a compact Riemann surface, where is a real reductive Lie group and is a holomorphic line bundle over. Evaluating the Higgs field … on a basis of the ring of polynomial invariants of the isotropy representation defines the Hitchin map.

Authors: Oscar García-Prada, Ana Peón-Nieto, S. Ramanan

Date Published: 1st Apr 2018

Publication Type: Journal

The pressure metric on the Margulis multiverse

Abstract (Expand)

This paper defines the pressure metric on the Moduli space of Margulis spacetimes without cusps and shows that it is positive definite on the constant entropy sections. It also demonstrates an identity … regarding the variation of the cross-ratios.

Author: Sourav Ghosh

Date Published: 1st Apr 2018

Publication Type: Journal

Convex projective generalized Dehn filling

Abstract (Expand)

For d = 4,5,6, we exhibit the first examples of complete finite volume hyperbolic d-manifolds M with cusps such that infinitely many d-orbifolds M_m obtained from M by generalized Dehn filling admit … properly convex real projective structures. The orbifold fundamental groups of M_m are Gromov-hyperbolic relative to a collection of subgroups virtually isomorphic to \mathbbZ^d-2, hence the images of the developing maps of the projective structures on M_m are new examples of divisible properly convex domains of the projective d-space which are not strictly convex, in contrast to the previous examples of Benoist.

Authors: Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis

Date Published: 30th Mar 2018

Publication Type: Journal

Deforming convex real projective structures

Abstract (Expand)

Let S be a closed, connected, orientable surface of genus at least 2, and let C(S) denote the deformation space of convex real projective structures S. In this article, we introduce two new flows on … C(S), which we call the internal bulging flow and the eruption flow. These are geometrically defined flows associated to each pair of pants in a pants decomposition on S that deform the internal parameters. We show that the eruption flows, together with the generalized twist flows about the pants curves, give rise to a half-dimensional family of commuting flows on C(S).

Authors: Anna Wienhard, Tengren Zhang

Date Published: 1st Feb 2018

Publication Type: Journal

Powered by
 (v.1.14.2)
About HITS Publication SEEK | About HITS-Publication-SEEK | Funding and Programmes | Credits
Copyright © 2008 - 2023 The University of Manchester and HITS gGmbH