Title :

Sur les fonctions de Dehn des produits centraux de groupes nilpotents

Author(s) :

García-Mejía, Jerónimo [Auteur]
Karlsruhe Institute of Technology = Karlsruher Institut für Technologie [KIT]
Isenrich, Claudio Llosa [Auteur]
Karlsruhe Institute of Technology = Karlsruher Institut für Technologie [KIT]
Pallier, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille

English keyword(s) :

Dehn functions
filling invariants
asymptotic cones
nilpotent groups
Lie groups and Lie algebras
central extensions
Quasiisometry
Carnot gradings
Group cohomology
sublinear bilipschitz equivalence
Heisenberg group

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We determine the Dehn functions of central products of two families of filiform nilpotent Lie groups of arbitrary dimension with all simply connected nilpotent Lie groups with cyclic centre and strictly lower nilpotency ...
Show more >We determine the Dehn functions of central products of two families of filiform nilpotent Lie groups of arbitrary dimension with all simply connected nilpotent Lie groups with cyclic centre and strictly lower nilpotency class. We also determine the Dehn functions of all central products of nilpotent Lie groups of dimension at most $5$ with one-dimensional centre. This confirms a conjecture of Llosa Isenrich, Pallier and Tessera for these cases, providing further evidence that the Dehn functions of central products are often strictly lower than those of the factors. Our work generalises previous results of Llosa Isenrich, Pallier and Tessera and produces an uncountable family of nilpotent Lie groups without lattices whose Dehn functions are strictly lower than the ones of the associated Carnot-graded groups. A consequence of our main result is the existence of an infinite family of groups such that Cornulier's bounds on the $e$ for which there is an $O(r^e)$-bilipschitz equivalence between them and their Carnot-graded groups are asymptotically optimal, as the nilpotency class goes to infinity.Show less >

Language :

Anglais

Comment :

56 pages, 4 figures, 2 tables. Comments welcome. v2: new Theorem VI and moved Appendix B.2 into a new Section 6

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL