Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The homotopy fixed point set of Lie group actions on elliptic spaces   Let $G$ be a compact connected Lie group, or more generally a path connected
topological group of the homotopy type of a finite CW-complex, and let $X$ be a
rational nilpotent $G$-space. In this paper we analyze the homotopy type of the
homotopy fixed point set $X^{hG}$, and the natural injection $k\colon
X^G\hookrightarrow X^{hG}$. We show that if $X$ is elliptic, that is, it has
finite dimensional rational homotopy and cohomology, then each path component
of $X^{hG}$ is also elliptic. We also give an explicit algebraic model of the
inclusion $k$ based on which we can prove, for instance, that for $G$ a torus,
$\pi_*(k)$ is injective in rational homotopy but, often, far from being a
rational homotopy equivalence.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
19
The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph