Pierre-Emmanuel Caprace

[Pierre-Emmanuel Caprace] [Research group] [Seminar]

Publications and preprints

Amalgams of rational unipotent groups and residual nilpotence (with Timothée Marquis).
Preprint (2024), 24 pages. arXiv
Lattice envelopes of right-angled Artin groups (with Tom De Medts).
Preprint (2024), 33 pages. arXiv
Simple p-adic Lie groups with abelian Lie algebras (with Ashot Minasyan and Denis Osin).
Preprint (2023), 31 pages. arXiv
On compact uniformly recurrent subgroups (with Gil Goffer and Waltraud Lederle).
Preprint (2022), 17 pages. arXiv
Tame automorphism groups of polynomial rings with property (T) and infinitely many alternating group quotients (with Martin Kassabov).
Trans. Amer. Math. Soc. 376 (2023), no. 11, pp. 7983–8021. arXiv | doi
Hyperbolic actions of higher-rank lattices come from rank-one factors (with Uri Bader, Alex Furman and Alessandro Sisto).
Preprint (2022), 20 pages. arXiv
Locally normal subgroups and ends of locally compact Kac-Moody groups (with Timothée Marquis and Colin Reid).
Münster J. Math. 15 (2022), no. 2, pp. 473–498. arXiv
Growing trees from compact subgroups (with Timothée Marquis and Colin Reid).
To appear in Groups Geom. Dyn. Preprint (2021), 20 pages. arXiv
A totally disconnected invitation to locally compact groups (with George Willis).
Preprint (2021), prepared for the proceedings of the ICM2022, 25 pages. arXiv
A type I conjecture and boundary representations of hyperbolic groups (with Mehrdad Kalantar and Nicolas Monod).
Proc. London Math. Soc. 127 (2023), no. 2, pp. 447–486. arXiv | doi
Piecewise strongly proximal actions, free boundaries and the Neretin groups (with Adrien Le Boudec and Nicolás Matte Bon).
Bull. Soc. Math. France 150 (2022), no. 4, pp. 773–795. arXiv | doi
Hyperbolic generalized triangle groups, property (T) and finite simple quotients (with Marston Conder, Marek Kaluba and Stefan Witzel).
J. London Math. Soc. 106, Nr. 4 (2022), pp. 3577–3637. arXiv | doi
Commensurated subgroups and micro-supported actions (with Adrien Le Boudec, and with an appendix by Dominik Francoeur).
J. Eur. Math. Soc. (JEMS) 25 (2023), no. 6, pp. 2251–2294. arXiv | doi
Closed sets of real roots in Kac-Moody root systems (with Timothée Marquis).
Preprint (2018), 8 pages. arXiv
A radius 1 irreducibility criterion for lattices in products of trees.
Ann. H. Lebesgue. Preprint 5 (2022), pp. 643–675. arXiv | doi
Groups with irreducibly unfaithful subsets for unitary representations (with Pierre de la Harpe).
Confluentes Math. 12, Nr. 1 (2020), pp. 31–68. arXiv
Bounding the covolume of lattices in products (with Adrien Le Boudec).
Compos. Math. 155 (2019), no. 12, 2296–2333. Preprint (2018), 51 pages. arXiv | doi
Almost simplicity of commensurators of free groups.
Six-page appendix to the paper New simple lattices in products of trees and their projections by Nicolas Radu.
Canad. J. Math. 72 (2020), no. 6, 1624–1690. arXiv | doi
Finite and infinite quotients of discrete and indiscrete groups.
in: Groups St Andrews 2017 in Birmingham, 1669, London Math. Soc. Lecture Note Ser., 455, Cambridge Univ. Press, Cambridge, 2019. arXiv
A sixteen-relator presentation of an infinite hyperbolic Kazhdan group.
Enseign. Math. 64 (2018), no. 34, 265–282. arXiv | doi
Future directions in locally compact groups: a tentative problem list. (with Nicolas Monod).
in: New directions in locally compact groups, 343–355, London Math. Soc. Lecture Note Ser., 447, Cambridge Univ. Press, Cambridge, 2018. arXiv
Indicability, residual finiteness, and simple subquotients of groups acting on trees (with Phillip Wesolek).
Geom. Topol. 22 (2018), no. 7, 4163–4204. arXiv | doi
Approximating simple locally compact groups by their dense locally compact subgroups (with Colin Reid and Phillip Wesolek).
Int. Math. Res. Not. 2021 Nr. 7 (2021), pp. 5037–5110 arXiv | doi
On the residual and profinite closures of commensurated subgroups (with Peter Kropholler, Colin Reid and Phillip Wesolek).
Math. Proc. Cambridge Philos. Soc. 169, Nr. 2 (2020), pp. 411–432. arXiv | doi
Lattices in amenable groups (with Uri Bader, Tsachik Gelander and Shahar Mozes).
Fund. Math. 246 (2019), no. 3, 217–255. arXiv
Non-discrete simple locally compact groups.
in: European Congress of Mathematics, Berlin 1822, 2016, pp. 333–354. Eur. Math. Soc., Zürich, 2018. pdf
On the linearity of lattices in affine buildings and ergodicity of the singular Cartan flow (with Uri Bader and Jean Lécureux).
J. Amer. Math. Soc. 32, Nr. 2 (2019), pp. 491–562. arXiv | doi
Chabauty limits of simple groups acting on trees (with Nicolas Radu).
J. Inst. Math. Jussieu 19, Nr. 4 (2020), pp. 1093–1120. arXiv | doi
An indiscrete Bieberbach theorem: from amenable CAT(0) groups to Tits buildings (with Nicolas Monod).
J. Éc. polytech. Math. 2 (2015), pp. 333–383. arXiv | doi
Totally disconnected locally compact groups with a linear open subgroup (with Thierry Stulemeijer).
Int. Math. Res. Not. 2015 Nr. 24 (2015), pp. 13800–13829. arXiv | doi
Orthogonal forms of Kac-Moody groups are acylindrically hyperbolic (with David Hume).
Ann. Inst. Fourier 65 Nr. 6 (2015), pp. 2613–2640. arXiv | doi
Boundary stabilisers in CAT(0) cube complexes.
Four-page appendix to the paper The median class and superrigidity of actions on CAT(0) cube complexes
by Indira Chatterji, Talia Fernos and Alesssandra Iozzi. arXiv | doi
Boundary Moufang trees with abelian root groups of characteristic p (with Matthias Grüninger).
Preprint (2014), 29 pages. arXiv
Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups (with Colin Reid and George Willis).
Forum Math. Sigma 5 (2017), e12, 89 pp. arXiv | doi
Locally normal subgroups of totally disconnected groups. Part I: General theory (with Colin Reid and George Willis).
Forum Math. Sigma 5 (2017), e11, 76 pp. arXiv | doi
Generalizing to all Coxeter groups (with Jason Behrstock, Mark Hagen and Alessandro Sisto).
Four-page appendix to the paper Thickness, relative hyperbolicity, and randomness in Coxeter groups by Behrstock, Hagen and Sisto. arXiv
Relative amenability (with Nicolas Monod).
Groups Geom. Dyn. 8 Nr. 3 (2014), pp. 747–774. arXiv | doi
Limits of contraction groups and the Tits core (with Colin Reid and George Willis).
J. Lie Theory 24 Nr. 4 (2014), pp. 957–967. arXiv
Gelfand pairs and strong transitivity for Euclidean buildings (with Corina Ciobotaru).
Ergodic Theory Dynam. Systems 35 (2015), Nr. 4, 1056–1078. arXiv
Locally normal subgroups of simple locally compact groups (with Colin Reid and George Willis).
C. R. Acad. Sci. Paris, Ser. I, 351 Nr. 1718 (2013), pp. 657–661. arXiv | doi
Automorphism groups of right-angled buildings: simplicity and local splittings.
Fund. Math. 224 (2014), pp. 17–51. pdf | arXiv | doi
On conjugacy separability of some Coxeter groups and parabolic-preserving automorphisms (with Ashot Minasyan).
Illinois J. Math. 57 Nr. 2 (2013), pp. 499–523. pdf | arXiv
Simplicity of twin tree lattices with non-trivial commutation relations (with Bertrand Rémy).
in Topology and geometric group theory, Springer Proc. Math. Stat. 184 (2016), pp. 143–151. pdf | arXiv
On embeddings into compactly generated groups (with Yves de Cornulier).
Pacific J. Math. 269 Nr. 2 (2014), pp. 305–322. pdf | arXiv | doi
Lectures on CAT(0) spaces and their isometry groups.
Based on lectures given at PCMI 2012, published in the volume
Geometric group theory, pp. 91–125, IAS/Park City Math. Ser., 21, Amer. Math. Soc., Providence, RI, 2014. pdf
Fixed points and amenability in non-positive curvature (with Nicolas Monod).
Math. Ann. 356 Nr. 4 (2013), pp. 1303–1337. pdf | doi | arXiv
Amenable hyperbolic groups (with Yves de Cornulier, Nicolas Monod and Romain Tessera).
J. Eur. Math. Soc. (JEMS) 17 (2015), Nr. 11, 2903–2947. arXiv
Trees, contraction groups and Moufang sets (with Tom De Medts).
Duke Math. J. 162 Nr. 13 (2013), pp. 2413–2449 pdf | arXiv
Regular elements in CAT(0) groups (with Gaper Zadnik).
Groups Geom. Dyn. 7 (2013), Nr. 3, 535–541 pdf | arXiv
Open subgroups of locally compact KacMoody groups (with Timothée Marquis).
Math. Z. 274 Nr. 1 (2013), pp. 291–313 pdf | doi | arXiv
Simple groups without lattices (with Uri Bader, Tsachik Gelander and Shahar Mozes).
Bull. Lond. Math. Soc. 44 Nr. 1, (2012), pp. 55–67. pdf | doi | arXiv
Rank rigidity for CAT(0) cube complexes (with Michah Sageev).
Geom. Funct. Anal. 21 Nr. 4 (2011) pp. 851–891. pdf | doi | arXiv
Simple locally compact groups acting on trees and their germs of automorphisms (with Tom De Medts).
Transform. Groups 16 Nr. 2 (2011) pp. 375–411. pdf | doi | arXiv
Bipolar Coxeter groups (with Piotr Przytycki).
J. Algebra 338 Nr. 1 (2011) pp. 35–55. pdf | doi | arXiv
Twist-rigid Coxeter groups (with Piotr Przytycki).
Geometry & Topology 14 (2010) pp. 2243–2275. pdf | doi | arXiv
Twin building lattices do not have asymptotic cut-points (with François Dahmani and Vincent Guirardel).
Geom. Dedicata. 147 Nr. 1 (2010), pp. 409–415. pdf | doi | arXiv
Non-distortion of twin building lattices (with Bertrand Rémy).
Geom. Dedicata. 147 Nr. 1 (2010), pp. 397–408. pdf | doi | arXiv
Can an anisotropic reductive group admit a Tits system? (with Timothée Marquis).
Pure and Appl. Math. Quart. 7 Nr. 3 (2011), pp. 539–558. pdf | arXiv
Combinatorial and group-theoretic compactifications of buildings (with Jean Lécureux).
Ann. Inst. Fourier 61 Nr. 2 (2011), pp. 619–672. pdf | doi | arXiv
A lattice in more than two KacMoody groups is arithmetic (with Nicolas Monod).
Israel J. Math. 190 (2012), pp. 413–444. pdf | doi | arXiv
Decomposing locally compact groups into simple pieces (with Nicolas Monod).
Math. Proc. Cambridge Philos. Soc. 150 Nr. 1 (2011), pp. 97–128. pdf | doi | arXiv | Corrigendum: pdf | doi
At infinity of finite-dimensional CAT(0) spaces (with Alexander Lytchak).
Math. Ann. 346 Nr. 1 (2010), pp. 1–21. pdf | doi | arXiv

Isometry groups of non-positively curved spaces: discrete subgroups (with Nicolas Monod).
J. Topology. 2 Nr. 4 (2009) 701–746. pdf | doi | arXiv | Erratum and addenda: arXiv

Isometry groups of non-positively curved spaces: structure theory (with Nicolas Monod).
J. Topology. 2 Nr. 4 (2009) 661–700. pdf | doi | arXiv

Rank one isometries of buildings and quasi-morphisms of KacMoody groups (with Koji Fujiwara).
Geom. Funct. Anal. 19 Nr. 5 (2010) 1296–1319. pdf | doi | arXiv

Some properties of non-positively curved lattices (with Nicolas Monod).
C. R. Acad. Sci. Paris, Ser. I 346 No. 1516 (2008), pp. 857–862. pdf | doi | arXiv

Amenable groups and Hadamard spaces with a totally disconnected isometry group.
Comment. Math. Helv. 84 Nr. 2 (2009), pp. 437–455. pdf | doi | arXiv

Buildings with isolated subspaces and relatively hyperbolic Coxeter groups.
Proceedings of the conference Buildings & Groups held in Ghent in May 2007.
Innov. Incidence Geom. 10 (2009), pp. 15–31. With an erratum | arXiv

A uniform bound on the nilpotency degree of certain subalgebras of KacMoody algebras.
J. Algebra 317 Nr. 2 (2007), pp. 867–876. pdf | doi | arXiv

Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls.
Algebraic & Geometric Topology 6 (2006), pp. 1987–2029. pdf | doi | arXiv

[This is a completely revised version of an earlier preprint which was circulated under the title Reflection triangles and parallel walls in Coxeter complexes, available here: pdf ]

Simplicity and superrigidity of twin building lattices (with Bertrand Rémy).
Invent. Math. 176 Nr. 1 (2009), pp. 169–221. pdf | doi | arXiv

Groups with a root group datum (with Bertrand Rémy).
Innov. Incidence Geom. 9 (2009), pp. 5–77. pdf

[Based on two series of lectures, the first one given in the Advanced Class in Algebra at the University of Oxford, Hilary term 2007 and the second given jointly with Bertrand Rémy at the conference Buildings and Groups in Ghent, May 2007. ]

On geometric flats in the CAT(0) realization of Coxeter groups and Tits buildings (with Frédéric Haglund).
Canad. J. Math. Vol. 61 Nr. 4, 2009 pp. 740–761. pdf | arXiv

Simplicité abstraite des groupes de KacMoody non affines (with Bertrand Rémy).
C. R. Acad. Sci. Paris, Ser. I 342 Nr. 8 (2006), pp. 539–544. pdf | doi

``Abstract'' homomorphisms of split KacMoody groups.
Memoir of the AMS 198 (2009), 84 pp. pdf | AMS

Reflection rigidity of 2-spherical Coxeter groups (with Bernhard Mühlherr).
Proc. London Math. Soc. 94 Nr. 2 (2007), pp. 520–542. pdf | doi

Isomorphisms of KacMoody groups which preserve bounded subgroups (with Bernhard Mühlherr).
Adv. Math. 206 (2006), pp. 250–278. pdf | doi | arXiv

On 2-spherical KacMoody groups and their central extensions.
Forum Math. 19 (2007), pp. 763–781. pdf | doi

Isomorphisms of KacMoody groups (with Bernhard Mühlherr).
Invent. Math. 161 Nr. 2 (2005), pp. 361–388. pdf | doi

Primitive symmetric spaces.
Bull. Belgian Math. Soc. 12 Nr. 3 (2005), pp. 321–328. pdf | doi

Reflection triangles in Coxeter groups and biautomaticity (with Bernhard Mühlherr).
J. Group Theory 8 Nr. 4 (2005), pp. 467–489. pdf | doi

The thick frame of a weak twin building.
Adv. Geom. 5 Nr. 1 (2005), pp. 119–136. pdf | doi