Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost fixed points of finite group actions on manifolds without odd
  cohomology   If $X$ is a smooth manifold and ${\mathcal{G}}$ is a subgroup of $Diff(X)$ we
say that $(X,{\mathcal{G}})$ has the almost fixed point property if there
exists a number $C$ such that for any finite subgroup $G\leq{\mathcal{G}}$
there is some $x\in X$ whose stabilizer $G_x\leq G$ satisfies $[G:G_x]\leq C$.
We say that $X$ has no odd cohomology if its integral cohomology is torsion
free and supported in even degrees. We prove that if $X$ is compact and
possibly with boundary and has no odd cohomology then $(X,Diff(X))$ has the
almost fixed point property. Combining this with a result of Petrie and Randall
we conclude that if $Z$ is a non necessarily compact smooth real affine
variety, and $Z$ has no odd cohomology, then $(Z,Aut(Z))$ has the almost fixed
point property, where $Aut(Z)$ is the group of algebraic automorphisms of $Z$
lifting the identity on $Spec\,{\mathbb{R}}$.

16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th