Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimations de dimensions de Minkowski dans l'espace des groupes
  marqu\'es   Dans cet article, on montre que l'espace des groupes marqu\'es est un
sous-espace ferm\'e d'un ensemble de Cantor dont la dimension de Hausdorff est
infinie.
  On prouve que la dimension de Minkowski de cet espace est infinie en exhibant
des sous-ensembles de groupes marqu\'es \`a petite simplification dont les
dimensions de Minkowski sont arbitrairement grandes.
  On donne une estimation des dimensions de Minkowski de sous-espaces de
groupes \`a un relateur.
  On d\'emontre enfin que les dimensions de Minkowski du sous-espace des
groupes commutatifs marqu\'es et d'un ensemble de Cantor d\'efini par
Grigorchuk sont nulles. // // // In this article we show that the space of
marked groups is a closed subspace of a Cantor space with infinite Hausdorff
dimension. We prove that the Minkowski dimension of this space is infinite by
exhibiting subsets of marked groups with small cancellation the dimensions of
which are arbitrarly large. We give estimates of the Minkowski dimensions of of
subsets of marked groups with one relator. Eventually, we prove that the
Minkowski dimensions of the subspace of abelian marked groups and a Cantor
space defined by Grigorchuk are zero.

32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio