Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The structure theory of Nilspaces III: Inverse limit representations and
  topological dynamics   This paper forms the third part of a series by the authors [GMV1,GMV2]
concerning the structure theory of nilspaces. A nilspace is a compact space $X$
together with closed collections of cubes $C^n(X)\subseteq X^{2^n}$,
$n=1,2,\ldots$, satisfying some natural axioms. Our goal is to extend the
structure theory of nilspaces obtained by Antol\'in Camarena and Szegedy, and
to provide new proofs.
  Our main result is that, under the technical assumption that $C^n(X)$ is a
connected space for all $n$, then $X$ is isomorphic (in a strong sense) to an
inverse limit of nilmanifolds. This is a direct and slight generalization of
the main result of Antol\'in Camarena and Szegedy.
  We also apply our methods to obtain structure theorems in the setting of
topological dynamics. Specifically, if $H$ is a group (subject to very mild
topological assumptions) and $(H,X)$ is a minimal dynamical system, then we
give a simple characterization of the maximal pronilfactor of $X$. This
generalizes the case $H = \mathbb{Z}$, which is a theorem of Host, Kra and
Maass, although even in that case we give a significantly different proof.

11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph