Min Yan
Functoriality of Isovariant Homotopy Classification.
Tue, 09/29/2009 - 15:21 — SomNambulAuthors: Sylvain Cappell, Shmuel Weinberger, Min Yan
Subjects: Geometric Topology
AbstractIt is a deep fact that the homotopy classification of topological manifolds
is convariantly functorial. In other words, a map from a topological manifold M
to another N naturally induces a map from the structure set S(M) to S(N). We
extend the fact to the isovariant structure set S_G(M, rel M_s) of
G-equivariant topological manifolds isovariantly homotopy equivalent to M and
restricts to homormorphism on the singular part M_s, consisting of those points
fixed by some non-trivial elements of G.Replacement of fixed sets for compact group actions: The 2\rho theorem.
Tue, 09/29/2009 - 15:21 — SomNambulAuthors: Sylvain Cappell, Shmuel Weinberger, Min Yan
Subjects: Geometric Topology
AbstractIf 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.
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