The real spectrum compactification of character varieties: characterizations and applications

Marc Burger, Alessandra Iozzi, Anne Parreau, Maria Beatrice Pozzetti

Type: Article

Publication Date: 2021-06-17

Citations: 9

DOI: https://doi.org/10.5802/crmath.123

Abstract

We announce results on a compactification of general character varieties that has good topological properties and give various interpretations of its ideal points. We relate this to the Weyl chamber length compactification and apply our results to the theory of maximal and Hitchin representations.

Locations

Comptes Rendus Mathématique - View - PDF
arXiv (Cornell University) - View - PDF
French digital mathematics library (Numdam) - View - PDF
Repository for Publications and Research Data (ETH Zurich) - View - PDF

Similar Works

Action	Title	Year	Authors
+	The real spectrum compactification of character varieties: characterizations and applications	2020	Marc Burger Alessandra Iozzi Anne Parreau Marie Beatrice Pozzetti
+	The real spectrum compactification of character varieties: characterizations and applications	2020	Marc Burger Alessandra Iozzi Anne Parreau Marie Beatrice Pozzetti
+	The real spectrum compactification of character varieties	2023	Marc Burger Alessandra Iozzi Anne Parreau Maria Beatrice Pozzetti
+ PDF Chat	Compactification of varieties	1990	Niels Schwartz
+ PDF Chat	The real spectrum and the oriented Gromov--Hausdorff compactifications of character varieties	2024	Victor Jaeck
+	A directional compactification of the complex Bloch variety	1990	Horst Knörrer Eugene Trubowitz
+	A directional compactification of the complex bloch variety	1993	A Franz
+ PDF Chat	The Length Spectrum of a Compact Constant Curvature Complex is Discrete	2006	Noel Brady Jon McCammond
+	Compactification of Spaces of Representations After Culler, Morgan and Shalen	2014	Jean-Pierre Otal
+	Compactification of Strictly Convex Real Projective Structures	2005	Инканг Ким
+ PDF Chat	Compactification d’espaces de représentations de groupes de type fini	2011	Anne Parreau
+	A compactification of the complement of a secant variety	1989	Aaron Bertram
+	Compactification of the moduli of abelian varieties	1996	Iku Nakamura
+	Cellulation of Compactified Hurwitz Spaces	2003	Michel Imbert
+	Des notions sur la géométrie hyperbolique complexe	2008	Tarik Jari
+	Intersection theory on Deligne-Mumford compactifications	1993	Eduard Looijenga
+	Complex analytic compactifications of ℂ3	1990	Mikio Furushima
+ PDF Chat	The Geometry of the Compactification of the Hurwitz Scheme	1995	Shinichi Mochizuki
+	Hyperbolicité complexe et quotients de domaines symétriques bornés	2018	Benoît Cadorel
+ PDF Chat	None	2023	Lucas Mason-Brown

Works That Cite This (9)

Action	Title	Year	Authors
+ PDF Chat	A closed ball compactification of a maximal component via cores of trees	2024	Giuseppe Martone Charles Ouyang Andrea Tamburelli
+	Subset currents on surfaces	2022	Dounnu Sasaki
+ PDF Chat	Hitchin representations of Fuchsian groups	2023	Richard D. Canary
+ PDF Chat	Length spectrum compactification of the SO0(2,3)-Hitchin component	2023	Charles Ouyang Andrea Tamburelli
+	Length spectrum compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component	2020	Charles Ouyang Andrea Tamburelli
+ PDF Chat	Currents, systoles, and compactifications of character varieties	2021	M. Burger Alessandra Iozzi Anne Parreau Maria Beatrice Pozzetti
+	Positive crossratios, barycenters, trees and applications to maximal representations	2024	Marc Burger Alessandra Iozzi Anne Parreau Maria Beatrice Pozzetti
+	An incomplete real tree with complete segments	2022	Raphael Appenzeller Luca De Rosa Xenia Flamm Victor Jaeck
+ PDF Chat	Dominating surface-group representations via Fock–Goncharov coordinates	2025	P Barman Subhojoy Gupta

Works Cited by This (30)

Action	Title	Year	Authors
+ PDF Chat	Cross ratios, Anosov representations and the energy functional on Teichmüller space	2008	François Labourie
+	Commutative Algebra: Chapters 1-7	1972	Nicolás Bourbaki
+ PDF Chat	Global existence theorems for harmonic maps to non-locally compact spaces	1997	Nicholas J. Korevaari Richard Schoen
+	Minimum Vectors for Real Reductive Algebraic Groups	1990	R. W. Richardson Peter Slodowy
+ PDF Chat	Surface group representations with maximal Toledo invariant	2010	Marc Burger Alessandra Iozzi Anna Wienhard
+ PDF Chat	Connected components of the compactification of representation spaces of surface groups	2011	Maxime Wolff
+ PDF Chat	Compactification via le spectre réel d'espaces des classes de représentation dans SO$(n,1)$	1994	Taoufik Bouzoubaa
+ PDF Chat	The ultrafilter theorem in real algebraic geometry	1989	G. W. Brumfiel
+	The geometry of Teichm�ller space via geodesic currents	1988	Francis Bonahon
+	Cocycles, Hausdorff measures and cross ratios	1997	Ursula Hamenstädt