Complex homogeneous manifolds with two ends.

Three-Manifolds and Manifolds with Cylindrical Ends

Contents Introduction. 1 Chapter 1. Four-dimensional Theory. 4 1. Setup. 4 2. A slice theorem for singular connections. 9 3. Laplacians on forms. 17 Chapter 2. Three-dimensional Theory. 22 1. Setup. 22 2. The Chern-Simons functional. 24 3. The deformation complex. 27 Chapter 3. Singular connections on manifolds with cylindrical ends. 33 1. Setup. 33 2. The translation-invariant case. 35 3. Glob...

Homogeneous two-manifolds with an invariant two-form

We study a 2-dimensional manifold that is homogeneous acted on by a 3-dimensional Lie group G, and that has a 2-form invariant under G. We show that such a manifold can be realized as a surface in the affine 3-space and list such realizations. Mathematics Subject Classification(2000). 53C30, 53C42, 53C45

A Note on Homogeneous Complex Contact Manifolds

Almost Homogeneous Manifolds with Boundary

In this article we study the classification of some Lie group actions on differentiable manifolds, up to conjugacy. Let us start with the precise notion of conjugacy we shall use. Two C r actions ρ1, ρ2 of a Lie group G on a manifold M are said to be C r conjugate if there is a C r diffeomorphism Φ : M → M that is (ρ1, ρ2) equivariant, that is: Φ(ρ1(g)x) = ρ2(g)Φ(x) ∀x ∈ M ∀g ∈ G. A conjugacy c...

Dirac operators on manifolds with periodic ends

This paper studies Dirac operators on end-periodic spin manifolds of dimension at least 4. We provide a necessary and sufficient condition for such an operator to be Fredholm for a generic end-periodic metric. We make use of end-periodic Dirac operators to give an analytical interpretation of an invariant of non-orientable smooth 4-manifolds due to Cappell and Shaneson. From this interpretation...