{"id":{"repo_id":"purdue-thes","oai_identifier":"oai:docs.lib.purdue.edu:open_access_dissertations-1570"},"canonical_url":"https://search.dev.ndltd.org/etd/purdue-thes/oai:docs.lib.purdue.edu:open_access_dissertations-1570","repository":{"repo_id":"purdue-thes","name":"Purdue University","base_url":"https://docs.lib.purdue.edu/do/oai/"},"display":{"title":"Orderability and rigidity in contact geometry","abstract":"<p>We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold (&Sgr;, ξ = ker(α)). Previous results (see [1]) show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable (&Sgr;, α) with dim(&Sgr;) ≥ 7, there exists a Liouville-fillable contact structure ξ' on &Sgr; which admits no positive loop at all. Further, ξ' can be chosen to agree with ξ' on the complement of a Darboux ball. We then define a relative version of orderability for a Legendrian submanifold, and discuss the relationship between the two notions.</p>","abstract_html":"&lt;p&gt;We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold (&amp;Sgr;, ξ = ker(α)). Previous results (see [1]) show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable (&amp;Sgr;, α) with dim(&amp;Sgr;) ≥ 7, there exists a Liouville-fillable contact structure ξ&#x27; on &amp;Sgr; which admits no positive loop at all. Further, ξ&#x27; can be chosen to agree with ξ&#x27; on the complement of a Darboux ball. We then define a relative version of orderability for a Legendrian submanifold, and discuss the relationship between the two notions.&lt;/p&gt;","abstract_has_math":false,"creators":["Weigel, Peter"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Peter Albers","Laszlo Lempert","Steve Bell","Ralph Kaufmann"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-04-01T07:00:00Z","date_published":"2015-04-01T07:00:00Z","updated_at":"2026-07-24T03:53:41Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://docs.lib.purdue.edu/open_access_dissertations/589","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Peter Albers","Laszlo Lempert","Steve Bell","Ralph Kaufmann"]},{"key":"dc:creator","label":"Author","values":["Weigel, Peter"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://docs.lib.purdue.edu/open_access_dissertations/589"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold (&Sgr;, ξ = ker(α)). Previous results (see [1]) show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable (&Sgr;, α) with dim(&Sgr;) ≥ 7, there exists a Liouville-fillable contact structure ξ' on &Sgr; which admits no positive loop at all. Further, ξ' can be chosen to agree with ξ' on the complement of a Darboux ball. We then define a relative version of orderability for a Legendrian submanifold, and discuss the relationship between the two notions.</p>"]},{"key":"dc:title","label":"Title","values":["Orderability and rigidity in contact geometry"]}]}],"canonical_facts":{"dc:contributor":["Peter Albers","Laszlo Lempert","Steve Bell","Ralph Kaufmann"],"dc:creator":["Weigel, Peter"],"dc:description.abstract":["<p>We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold (&Sgr;, ξ = ker(α)). Previous results (see [1]) show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable (&Sgr;, α) with dim(&Sgr;) ≥ 7, there exists a Liouville-fillable contact structure ξ' on &Sgr; which admits no positive loop at all. Further, ξ' can be chosen to agree with ξ' on the complement of a Darboux ball. We then define a relative version of orderability for a Legendrian submanifold, and discuss the relationship between the two notions.</p>"],"dc:identifier":["https://docs.lib.purdue.edu/open_access_dissertations/589"],"dc:subject":["Mathematics"],"dc:title":["Orderability and rigidity in contact geometry"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:53:41Z"}