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

Daniel A. Ramras

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arXiv · 1006.0063

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

Daniel A. Ramras

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Abstract

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.

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Daniel A. Ramras. 2010-06-01. Invariant tubular neighborhoods in infinite-dimensional Riemannian geometry, with applications to Yang-Mills theory. https://arxiv.org/abs/1006.0063

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