Orbit maps of local S¹- actions on manifolds of dimension less than five

<p>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.</p> <p>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.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematical Sciences

Year

1975

Author dc:creator

• Fintushel, Ronald A.

Contributors dc:contributor

• Louis F. McAuley

• Manifolds (Mathematics)
• Topology

Repository record dc:identifier

https://orb.binghamton.edu/dissertation_and_theses/275

OAI identifier oai:identifier

oai:orb.binghamton.edu:dissertation_and_theses-1281