Spin-structures and proper group actions

Hyperk Ahler Structures and Group Actions

GROUP ACTIONS ON SPIN MANIFOLDS(i)

A generalization of the theorem of V. Bargmann concerning unitary and ray representations is obtained and is applied to the general problem of lifting group actions associated to the extension of structure of a bundle. In particular this is applied to the Poincare group ? of a Lorentz manifold M. It is shown that the topological restrictions needed to lift an action in ? are more stringent than...

Proper actions and proper invariant metrics

We show that if a locally compact group G acts properly on a locally compact σ-compact space X, then there is a family of G-invariant proper continuous finite-valued pseudometrics which induces the topology of X. If X is, furthermore, metrizable, then G acts properly on X if and only if there exists a G-invariant proper compatible metric on X.

On Symmetric Group S3 Actions on Spin 4-manifolds

Let X be a smooth, closed, connected spin 4-manifold with b1(X) = 0 and non-positive signature σ(X). In this paper we use Seiberg-Witten theory to prove that if X admits an odd type symmetric group S3 action preserving the spin structure, then b+2 (X) ≥ |σ(X)|/8 + 3 under some non-degeneracy conditions. We also obtain some information about IndS̃3 D, where S̃3 is the extension of S3 by Z2.

Singular Reduction for Proper Actions