Geometric presentations of Lie groups and their Dehn functions

Yves Cornulier; Romain Tessera

doi:10.1007/s10240-016-0087-3

Geometric presentations of Lie groups and their Dehn functions

Yves Cornulier
, Romain Tessera

Laboratoire de Mathématiques d'Orsay

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We study the Dehn function of connected Lie groups. We show that this function is always exponential or polynomially bounded, according to the geometry of weights and of the 2-cohomology of their Lie algebras. Our work, which also addresses algebraic groups over local fields, uses and extends Abels’ theory of multiamalgams of graded Lie algebras, in order to provide workable presentations of these groups.

Original language	English
Pages (from-to)	79-219
Number of pages	141
Journal	Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume	125
Issue number	1
DOIs	https://doi.org/10.1007/s10240-016-0087-3
Publication status	Published - 1 Jun 2017
Externally published	Yes

Access to Document

10.1007/s10240-016-0087-3

Cite this

@article{b2bb8061de7b4cbb9a18c2423184c86f,

title = "Geometric presentations of Lie groups and their Dehn functions",

abstract = "We study the Dehn function of connected Lie groups. We show that this function is always exponential or polynomially bounded, according to the geometry of weights and of the 2-cohomology of their Lie algebras. Our work, which also addresses algebraic groups over local fields, uses and extends Abels{\textquoteright} theory of multiamalgams of graded Lie algebras, in order to provide workable presentations of these groups.",

author = "Yves Cornulier and Romain Tessera",

note = "Publisher Copyright: {\textcopyright} 2016, IHES and Springer-Verlag Berlin Heidelberg.",

year = "2017",

month = jun,

day = "1",

doi = "10.1007/s10240-016-0087-3",

language = "English",

volume = "125",

pages = "79--219",

journal = "Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques",

issn = "0073-8301",

publisher = "Institut des Hautes {\'E}tudes Scientifiques",

number = "1",

}

TY - JOUR

T1 - Geometric presentations of Lie groups and their Dehn functions

AU - Cornulier, Yves

AU - Tessera, Romain

PY - 2017/6/1

Y1 - 2017/6/1

N2 - We study the Dehn function of connected Lie groups. We show that this function is always exponential or polynomially bounded, according to the geometry of weights and of the 2-cohomology of their Lie algebras. Our work, which also addresses algebraic groups over local fields, uses and extends Abels’ theory of multiamalgams of graded Lie algebras, in order to provide workable presentations of these groups.

AB - We study the Dehn function of connected Lie groups. We show that this function is always exponential or polynomially bounded, according to the geometry of weights and of the 2-cohomology of their Lie algebras. Our work, which also addresses algebraic groups over local fields, uses and extends Abels’ theory of multiamalgams of graded Lie algebras, in order to provide workable presentations of these groups.

U2 - 10.1007/s10240-016-0087-3

DO - 10.1007/s10240-016-0087-3

M3 - Article

AN - SCOPUS:85006835755

SN - 0073-8301

VL - 125

SP - 79

EP - 219

JO - Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques

JF - Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques

IS - 1

ER -

Geometric presentations of Lie groups and their Dehn functions

Abstract

Access to Document

Fingerprint

Cite this