Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant dimensions of groups with operators   Let $\pi$ be a group equipped with an action of a second group $G$ by
automorphisms. We define the equivariant cohomological dimension ${\sf
cd}_G(\pi)$, the equivariant geometric dimension ${\sf gd}_G(\pi)$, and the
equivariant Lusternik-Schnirelmann category ${\sf cat}_G(\pi)$ in terms of the
Bredon dimensions and classifying space of the family of subgroups of the
semi-direct product $\pi\rtimes G$ consisting of sub-conjugates of $G$. When
$G$ is finite, we extend theorems of Eilenberg-Ganea and Stallings-Swan to the
equivariant setting, thereby showing that all three invariants coincide (except
for the possibility of a $G$-group $\pi$ with ${\sf cat}_G(\pi)={\sf
cd}_G(\pi)=2$ and ${\sf gd}_G(\pi)=3$). A main ingredient is the purely
algebraic result that the cohomological dimension of any finite group with
respect to any family of proper subgroups is greater than one. This implies a
Stallings-Swan type result for families of subgroups which do not contain all
finite subgroups.

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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cs
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph