Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Replacement of fixed sets for compact group actions: The 2\rho theorem   If M and N are equivariantly homotopy equivalent G-manifolds, then the fixed
sets M^G and N^G are also homotopy equivalent. The replacement problem asks the
converse question: If F is homotopy equivalent to the fixed set M^G, is F = N^G
for a G-manifold equivariantly homotopy equivalent to M? We prove that for
locally linear actions on topological or PL manifolds by compact Lie groups,
the replacement is always possible if the normal bundle of the fixed set is
twice of a complex bundle over a 1-skeleton of the fixed set. Moreover, we also
study some specific examples, where the answer to the replacement problem
ranges from always possible to the rigidity.

16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org