Invariant tubular neighborhoods in infinite-dimensional Riemannian geometry, with applications to Yang-Mills theory

We present a new construction of tubular neighborhoods in (possibly infinite dimensional) Riemannian manifolds M , which allows us to show that if G is an arbitrary group acting isometrically on M , then every G -invariant submanifold with locally trivial normal bundle has a G -invariant total tubul...

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Bibliographic Details
Published inArchiv der Mathematik Vol. 96; no. 6; pp. 589 - 599
Main Author Ramras, Daniel A.
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.06.2011
Subjects
Mathematics
Mathematics and Statistics
Primary 58B20
58D27
Yang-Mills theory
Tubular neighborhood
Secondary 53C07
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Summary:We present a new construction of tubular neighborhoods in (possibly infinite dimensional) Riemannian manifolds M , which allows us to show that if G is an arbitrary group acting isometrically on M , then every G -invariant submanifold with locally trivial normal bundle has a G -invariant total tubular neighborhood. We apply this result to the Morse strata of the Yang-Mills functional over a closed surface. The resulting neighborhoods play an important role in calculations of gauge-equivariant cohomology for moduli spaces of flat connections over non-orientable surfaces.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-011-0239-0