Semi-free actions with manifold orbit spaces
Differential Geometry
2019-01-29 v2 Geometric Topology
Abstract
In this paper, we study smooth, semi-free actions on closed, smooth, simply connected manifolds, such that the orbit space is a smoothable manifold. We show that the only simply connected -manifolds admitting a smooth, semi-free circle action with fixed-point components of codimension are connected sums of -bundles over . Furthermore, the Betti numbers of the -manifolds and of the quotient -manifolds are related by a simple formula involving the number of fixed-point components. We also investigate semi-free actions on simply connected -manifolds with quotient a -manifold and show, in particular, that there are strong restrictions on the topology of the -manifold.
Cite
@article{arxiv.1805.03113,
title = {Semi-free actions with manifold orbit spaces},
author = {John Harvey and Martin Kerin and Krishnan Shankar},
journal= {arXiv preprint arXiv:1805.03113},
year = {2019}
}
Comments
22 pages; V2: Clarified the choice of section in the proof of Theorem B