Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finiteness properties of automorphism spaces of manifolds with finite
  fundamental group   Given a closed smooth manifold $M$ of even dimension $2n\ge6$ with finite
fundamental group, we show that the classifying space ${\rm BDiff}(M)$ of the
diffeomorphism group of $M$ is of finite type and has finitely generated
homotopy groups in every degree. We also prove a variant of this result for
manifolds with boundary and deduce that the space of smooth embeddings of a
compact submanifold $N\subset M$ of arbitrary codimension into $M$ has finitely
generated higher homotopy groups based at the inclusion, provided the
fundamental group of the complement is finite.

32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys