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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Three basic results for real analytic proper G-manifolds

Presented by "Soren Illman (University of Helsinki, Finland)",

13 June 2002 00:00 in CM221

" We will try to cover the main results of the paper: Soren Illman and Marja Kankaanrinta, Three basic results for real analytic
proper G-manifolds, Math. Ann. 316 (2000),169-183, and also say something about the preceding paper by the same authors
in Math. Ann. 316 (2000), 139-168. We are interested in the following three questions concerning real analytic proper G-manifolds.
(i) Given a real analytic manifold M together with a real analytic proper action of a Lie group G on M, does there exist a G-invariant
real analytic Riemannian metric on M ?
(ii) Can one approximate a G-equivariant smooth map between two real analytic proper G-manifolds by a G-equivariant real analytic
map ?
(iii) Suppose G is a linear Lie group and let M be a real analytic proper G-manifold with only finitely many orbit types. Does there then
exist a G-equivariant real analytic imbedding of M into some finite dimensional linear representation space for G ?

We prove that the answer to questions (i) and (ii) is affirmative when G is a linear Lie group, and in fact more generally when G can
be imbedded as a closed subgroup in Lie group with only finitely many connected components. We also prove that the answer to
question (iii) is yes."

Unusual time and day: 11:00 am

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