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.
","abstract_html":"<p>A local S<sup>1</sup>-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 S<sup>1</sup> 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 S<sup>1</sup>-action on M.</p> <p>This work provides a setting in which the orbit structure of locally smooth S<sup>1</sup>-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 S<sup>1</sup>-actions with orbit space M* and with PL orbit maps.</p>","abstract_has_math":false,"creators":["Fintushel, Ronald A."],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["Louis F. McAuley"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1975,"date_issued":"1975-01-01T08:00:00Z","date_published":"1975-01-01T08:00:00Z","updated_at":"2026-07-24T01:10:28Z","subjects":["Manifolds (Mathematics)","Topology"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://orb.binghamton.edu/dissertation_and_theses/275","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Louis F. McAuley"]},{"key":"dc:creator","label":"Author","values":["Fintushel, Ronald A."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Manifolds (Mathematics)","Topology"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://orb.binghamton.edu/dissertation_and_theses/275"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Orbit maps of local S¹- actions on manifolds of dimension less than five"]}]}],"canonical_facts":{"dc:contributor":["Louis F. McAuley"],"dc:creator":["Fintushel, Ronald A."],"dc:description.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.
"],"dc:identifier":["https://orb.binghamton.edu/dissertation_and_theses/275"],"dc:subject":["Manifolds (Mathematics)","Topology"],"dc:title":["Orbit maps of local S¹- actions on manifolds of dimension less than five"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T01:10:28Z"}