Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant cohomology of cohomogeneity one actions   We show that if $G\times M \to M$ is a cohomogeneity one action of a compact
connected Lie group $G$ on a compact connected manifold $M$ then $H^*_G(M)$ is
a Cohen-Macaulay module over $H^*(BG)$. Moreover, this module is free if and
only if the rank of at least one isotropy group is equal to the rank of $G$. We
deduce as corollaries several results concerning the usual (de Rham) cohomology
of $M$, such as the following obstruction to the existence of a cohomogeneity
one action: if $M$ admits a cohomogeneity one action, then $\chi(M)>0$ if and
only if $H^{\rm odd}(M)=\{0\}$.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs