Global and local equivariant characteristic numbers of G-manifolds

Equivariant Cohomology and Equivariant Characteristic Numbers of a Homogeneous Space

Let G be a compact connected Lie group with maximal torus T , and H a closed subgroup containing T . We compute the equivariant cohomology ring and the equivariant characteristic numbers of the homogeneous space G/H under the natural action of the maximal torus T . The computation is based on the localization theorems of Borel and of Atiyah-Bott-Berline-Vergne. Let G be a compact connected Lie ...

Curvature and Characteristic Numbers of Hyper-kähler Manifolds

Characteristic numbers of compact hyper-Kähler manifolds are expressed in graphtheoretical form, considering them as a special case of the curvature invariants introduced by L. Rozansky and E. Witten. The appropriate graphs are generated by “wheels,” and the recently proved Wheeling theorem is used to give a formula for the L 2-norm of the curvature of an irreducible hyper-Kähler manifold in te...

Local and Global Clique Numbers

Equivariant Tensors on Polar Manifolds

EQUIVARIANT TENSORS ON POLAR MANIFOLDS Ricardo Mendes Wolfgang Ziller, Advisor This PhD dissertation has two parts, both dealing with extension questions for equivariant tensors on a polar G-manifold M with section Σ ⊂ M. Chapter 3 contains the first part, regarding the so-called smoothness conditions: If a tensor defined only along Σ is equivariant under the generalized Weyl group W (Σ), then ...

Equivariant Deformations of Manifolds and Real Representations

In the paper we give a partial answer to the following question: let G be a finite group acting smoothly on a compact (smooth) manifold M , such that for each isotropy subgroup H of G the submanifold M fixed by H can be deformed without fixed points; is it true that then M can be deformed without fixed points G-equivariantly? The answer is no, in general. It is yes, for any G-manifold, if and o...