Abelian $p$-group actions on homology spheres

Group actions on homology spheres

This can be stated in a more symmetric manner. Let r be any positive integer not equal to 3. Then n acts freely and homologically trivially on Z r i ff n acts freely and homologically trivially on SL In fact, there is a one-to-one correspondence between such actions on U and such actions on S r. (The classification of such actions is discussed in w In addition the actions constructed have the p...

A Note on Group Actions on Homology Spheres

RANK THREE p-GROUP ACTIONS ON PRODUCTS OF SPHERES

Let p be an odd prime. We prove that every rank three p-group acts freely and smoothly on a product of three spheres. To construct this action, we first prove a generalization of a theorem of Lück and Oliver on constructions of G-equivariant vector bundles. We also give some other applications of this generalization.

Pseudofree Group Actions on Spheres

R. S. Kulkarni showed that a finite group acting pseudofreely, but not freely, preserving orientation, on an even-dimensional sphere (or suitable sphere-like space) is either a periodic group acting semifreely with two fixed points, a dihedral group acting with three singular orbits, or one of the polyhedral groups, occurring only in dimension 2. It is shown here that the dihedral group does no...

On the Homology Cobordism Group of Homology 3-spheres

In this paper we present our results on the homology cobordism group Θ3Z of the oriented integral homology 3-spheres. We specially emphasize the role played in the subject by the gauge theory including Floer homology and invariants by Donaldson and Seiberg – Witten. A closed oriented 3-manifold Σ is said to be an integral homology sphere if it has the same integral homology as the 3-sphere S. T...