Document Type

Dissertation

Date of Award

1975

Keywords

Manifolds (Mathematics), Topology

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Advisor

Louis F. McAuley

Abstract

A local S1-action on a topological space X is a decomposition of X into points and simple closed curves such that each element of the decomposition has an invariant neighborhood admitting an effective action of S1 whose orbits are elements of the decomposition. Let M be a compact connected PL n-manifold without boundary, and suppose that n ≤ 4. Let M* be a PL manifold of dimension n-1 and f a PL open map from M onto M* whose fibers are circles or points. It is proved that f is the orbit map of a local S1-action on M.

This work provides a setting in which the orbit structure of locally smooth S1-actions on PL 4-manifolds can be studied. Under certain conditions the orbit structure of such an action is shown to determine the action up to equivalence over the orbit space. More generally, given a 3-manifold M*, constructions are given for all locally smooth S1-actions with orbit space M* and with PL orbit maps.

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