A zoo of diffeomorphism groups on $$\mathbb{R }^{n}$$ R n

An Exotic Zoo of Diffeomorphism Groups on R

Let C[M ] be a (local) Denjoy–Carleman class of Beurling or Roumieu type, where the weight sequence M = (Mk) is log-convex and has moderate growth. We prove that the groups DiffB[M ](Rn), DiffW [M ],p(Rn), DiffS [M ] [L] (Rn), and DiffD[M ](Rn) of C[M ]-diffeomorphisms on Rn which differ from the identity by a mapping in B[M ] (global Denjoy– Carleman), W [M ],p (Sobolev–Denjoy–Carleman), S [M ...

Some properties of n-capable and n-perfect groups

In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.

n-cyclicizer groups

Limit groups and groups acting freely on R n-trees.

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R n-trees. We first prove that Sela's limit groups do have a free action on an R n-tree. We then prove that a finitely generated group having a free action on an R n-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic ...

Zoo of Lie n-Algebras

We present a menagerie of examples for Lie n-algebras, study their morphisms and discuss applications to higher order connections, in particular String 2-connections and Chern-Simons 3-connections.