Caprace, PierreEmmanuel 1981
Overview
Works:  8 works in 29 publications in 1 language and 441 library holdings 

Roles:  Author, Editor, Other, dgs, 958, Opponent 
Publication Timeline
.
Most widely held works by
PierreEmmanuel Caprace
"Abstract'' homomorphisms of split KacMoody groups by
PierreEmmanuel Caprace(
Book
)
12 editions published in 2009 in English and held by 252 WorldCat member libraries worldwide
12 editions published in 2009 in English and held by 252 WorldCat member libraries worldwide
New directions in locally compact groups by
Nicolas Monod(
Book
)
10 editions published in 2018 in English and Undetermined and held by 168 WorldCat member libraries worldwide
This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, padic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions
10 editions published in 2018 in English and Undetermined and held by 168 WorldCat member libraries worldwide
This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, padic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions
"Abstract" homomorphisms of split KacMoody groups by
PierreEmmanuel Caprace(
Book
)
2 editions published in 2009 in English and held by 13 WorldCat member libraries worldwide
2 editions published in 2009 in English and held by 13 WorldCat member libraries worldwide
Almost Automorphism Groups of Trees by
Waltraud Lederle(
Book
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Significance of flats in CAT(0) geometry : doctoral thesis by Gašper Zadnik(
Book
)
1 edition published in 2014 in English and held by 2 WorldCat member libraries worldwide
Številna vprašanja v CAT(0) geometriji izvirajo iz izrekov o Riemannovih mnogoterostih nepozitivnih prereznih ukrivljenosti. V disertaciji se ukvarjamo z enim izmed njih, s problemom periodičnih ravnin. V kontekstu realnih analitičnih mnogoterosti sta ga rešila Bangert in Schröder, [V Bangert, v Schröder, Existence of flat tori in analytic manifolds of nonpositive curvature. Ann. Sci. École Norm. Sup. 24 (1992), no. 4 pp. 605634]. Problem sprašuje, ali vedno lahko najdemo kopijo proste abelove grupe $\mathbb{Z}^m$ v grupi, ki deluje kokompaktno diskretno z izometrijami na CAT(0) prostoru $X$, ki vsebuje izometrično vloženo kopijo $\mathbb{R}^m$. V uvodnih poglavjih povzamemo dognanja iz del [P.E. Caprace, N. Monod, Isometry groups of nonpositively curved spaces: structure theory. J. Topol. 2 (2009), no. 4, pp. 661700 in P.E. Caprace, N. Monod, Isometry groups of nonpositively curved spaces: discrete subgroups. J. Topol. 2 (2009), no. 4, pp. 701746] o celotni grupi izometrij pravega kokompaktnega geodezično polnega CAT(0) prostora. Nato ta dognanja uporabimo v dokazu glavnega izreka iz [P.E. Caprace, G. Zadnik, Regular elements in CAT(0) groups. Preprint at http://arXiv.org/abs/1112.4637 (2011)], ki poda delni odgovor na problem periodičnih ravnin: "Naj bo parvi CAT(0) prostor $X$ produkt $m$ geodezično polnih faktorjev. Tedaj poljubna grupa $\Gamma$, ki deluje kokompaktno diskretno z izometrijami na $X$, vsebuje kopijo $\mathbb{Z}^m$." Čeprav predpostavke zapisanega izreka močno posežejo v splošnost problema periodičnih ravnin, so za njegov dokaz potrebni globoki izreki iz strukturne teorije grupe izometrij dotičnega CAT(0) prostora. Za dokaz ključna je rešitev Hilbertovega petega problema (izrek Glaeson, MontgomeryZippin), ki zagotavlja dihotomojo za grupe izometrij določenih CAT(0) prostorov. Bodisi je grupa izometrij Liejeva bodisi je popolnoma nepovezana lokalno kompaktna topološka grupa. Glede na to dihotomijo se dokaz izreka razdeli na dva dela. Prvi del sledi iz znanih izrekov iz teorije Liejevih grup, med tem ko se drugi del sklicuje na geometrijo CAT(0) prostora s popolnoma nepovezano grupo izometrij, [P.E. Caprace, N. Monod, Isometry groups of nonpositively curved spaces: structure theory. J. Topol. 2 (2009), no. 4, pp. 661700]
1 edition published in 2014 in English and held by 2 WorldCat member libraries worldwide
Številna vprašanja v CAT(0) geometriji izvirajo iz izrekov o Riemannovih mnogoterostih nepozitivnih prereznih ukrivljenosti. V disertaciji se ukvarjamo z enim izmed njih, s problemom periodičnih ravnin. V kontekstu realnih analitičnih mnogoterosti sta ga rešila Bangert in Schröder, [V Bangert, v Schröder, Existence of flat tori in analytic manifolds of nonpositive curvature. Ann. Sci. École Norm. Sup. 24 (1992), no. 4 pp. 605634]. Problem sprašuje, ali vedno lahko najdemo kopijo proste abelove grupe $\mathbb{Z}^m$ v grupi, ki deluje kokompaktno diskretno z izometrijami na CAT(0) prostoru $X$, ki vsebuje izometrično vloženo kopijo $\mathbb{R}^m$. V uvodnih poglavjih povzamemo dognanja iz del [P.E. Caprace, N. Monod, Isometry groups of nonpositively curved spaces: structure theory. J. Topol. 2 (2009), no. 4, pp. 661700 in P.E. Caprace, N. Monod, Isometry groups of nonpositively curved spaces: discrete subgroups. J. Topol. 2 (2009), no. 4, pp. 701746] o celotni grupi izometrij pravega kokompaktnega geodezično polnega CAT(0) prostora. Nato ta dognanja uporabimo v dokazu glavnega izreka iz [P.E. Caprace, G. Zadnik, Regular elements in CAT(0) groups. Preprint at http://arXiv.org/abs/1112.4637 (2011)], ki poda delni odgovor na problem periodičnih ravnin: "Naj bo parvi CAT(0) prostor $X$ produkt $m$ geodezično polnih faktorjev. Tedaj poljubna grupa $\Gamma$, ki deluje kokompaktno diskretno z izometrijami na $X$, vsebuje kopijo $\mathbb{Z}^m$." Čeprav predpostavke zapisanega izreka močno posežejo v splošnost problema periodičnih ravnin, so za njegov dokaz potrebni globoki izreki iz strukturne teorije grupe izometrij dotičnega CAT(0) prostora. Za dokaz ključna je rešitev Hilbertovega petega problema (izrek Glaeson, MontgomeryZippin), ki zagotavlja dihotomojo za grupe izometrij določenih CAT(0) prostorov. Bodisi je grupa izometrij Liejeva bodisi je popolnoma nepovezana lokalno kompaktna topološka grupa. Glede na to dihotomijo se dokaz izreka razdeli na dva dela. Prvi del sledi iz znanih izrekov iz teorije Liejevih grup, med tem ko se drugi del sklicuje na geometrijo CAT(0) prostora s popolnoma nepovezano grupo izometrij, [P.E. Caprace, N. Monod, Isometry groups of nonpositively curved spaces: structure theory. J. Topol. 2 (2009), no. 4, pp. 661700]
Géométrie des groupes localement compacts. Arbres. Action ! by
Adrien Le Boudec(
)
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
In Chapter 1 we investigate the class of locally compact lacunary hyperbolic groups. We characterize locally compact groups having one asymptotic cone that is a real tree and whose natural isometric action is focal. We also study the structure of lacunary hyperbolic groups, and prove that in the unimodular case subgroups cannot satisfy a law. We apply the previous results in Chapter 2 to solve the problem of the existence of cutpoints in asymptotic cones for connected Lie groups. In Chapter 3 we prove that Neretin's group is compactly presented and give an upper bound on its Dehn function. We also study metric properties of Neretin's group, and prove that some remarkable subgroups are quasiisometrically embedded. In Chapter 4 we study a family of groups acting on a tree, and whose local action is prescribed by some permutation group. We prove among other things that these groups have property (PW), and exhibit some simple groups in this family. In Chapter 5 we introduce the relation range of a finitely generated group, which is the set of lengths of relations that are not generated by relations of smaller length. We establish a link between simple connectedness of asymptotic cones and the relation range of the group, and give a large class of groups having a relation range as large as possible
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
In Chapter 1 we investigate the class of locally compact lacunary hyperbolic groups. We characterize locally compact groups having one asymptotic cone that is a real tree and whose natural isometric action is focal. We also study the structure of lacunary hyperbolic groups, and prove that in the unimodular case subgroups cannot satisfy a law. We apply the previous results in Chapter 2 to solve the problem of the existence of cutpoints in asymptotic cones for connected Lie groups. In Chapter 3 we prove that Neretin's group is compactly presented and give an upper bound on its Dehn function. We also study metric properties of Neretin's group, and prove that some remarkable subgroups are quasiisometrically embedded. In Chapter 4 we study a family of groups acting on a tree, and whose local action is prescribed by some permutation group. We prove among other things that these groups have property (PW), and exhibit some simple groups in this family. In Chapter 5 we introduce the relation range of a finitely generated group, which is the set of lengths of relations that are not generated by relations of smaller length. We establish a link between simple connectedness of asymptotic cones and the relation range of the group, and give a large class of groups having a relation range as large as possible
At infinity of finitedimensional CAT(0) spaces(
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
Regular elements in CAT(0) groups by
PierreEmmanuel Caprace(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Let $X$ be a locally compact geodesically complete CAT(0) space and $\Gamma$ be a discrete group acting properly and cocompactly on $X$. We show that $\Gamma$ contains an element acting as a hyperbolic isometry on each indecomposable de Rham factor of $X$. It follows that if $X$ is a product of $d$ factors, then $\Gamma$ contains $\mathbb{Z}^d$
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Let $X$ be a locally compact geodesically complete CAT(0) space and $\Gamma$ be a discrete group acting properly and cocompactly on $X$. We show that $\Gamma$ contains an element acting as a hyperbolic isometry on each indecomposable de Rham factor of $X$. It follows that if $X$ is a product of $d$ factors, then $\Gamma$ contains $\mathbb{Z}^d$
Audience Level
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Related Identities
 Monod, Nicolas 1973 Other Author Editor
 Laboratoire de mathématiques d'Orsay
 Cornulier, Yves de Opponent Thesis advisor
 Burger, Marc 1959
 Ecole doctorale Mathématiques de la région ParisSud (19922015 / Orsay)
 Zadnik, Gašper Author
 Lederle, Waltraud 1990 Author
 Université ParisSud Degree grantor
 Sapir, Mark (1957....).
 Breuillard, Emmanuel (1977....). Opponent
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