5 papers
Positivity and representations of surface groups
Olivier Guichard, François Labourie, Anna Wienhard
In arXiv:1802.02833 Guichard and Wienhard introduced the notion of -positivity, a generalization of Lusztig's total positivity to real Lie groups that are not necessarily split…
Noncommutative Polygonal Cluster Algebras
Zachary Greenberg, Dani Kaufman, Merik Niemeyer +1
We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein-…
Invariant multi-functions and Hamiltonian flows for surface group representations
Fernando Camacho-Cadena, James Farre, Anna Wienhard
Goldman defined a symplectic form on the smooth locus of the -character variety of a closed, oriented surface for a Lie group satisfying very general hypotheses. He then…
Positivity, cross-ratios and the Collar Lemma
Jonas Beyrer, Olivier Guichard, François Labourie +2
We prove that -positive representations of fundamental groups of surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and their associated cross-ratios are po…
Thurston's asymmetric metrics for Anosov representations
León Carvajales, Xian Dai, Beatrice Pozzetti +1
We provide a good dynamical framework allowing to generalize Thurston's asymmetric metric and the associated Finsler norm from Teichmüller space to large classes of Anosov represe…