In his seminal paper Infinitesimal Computations in Topology, Sullivan constructs algebraic models for spaces and then computes various invariants using them. In this thesis, we use those ideas to obtain a finiteness result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the space of almost complex structures on a manifold. As a special case, we discuss the space of almost complex structures on the six sphere and conclude a conjecture about the ordinary homotopy type of that space.
","abstract_html":"<p>In his seminal paper <em>Infinitesimal Computations in Topology</em>, Sullivan constructs algebraic models for spaces and then computes various invariants using them. In this thesis, we use those ideas to obtain a finiteness result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the space of almost complex structures on a manifold. As a special case, we discuss the space of almost complex structures on the six sphere and conclude a conjecture about the ordinary homotopy type of that space.</p>","abstract_has_math":false,"creators":["Ferlengez, Bora"],"institution":"The Graduate School and University Center of The City University of New York","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Dennis Sullivan"],"committee_chairs":[],"committee_members":["Martin Bendersky","James Simons","Scott Wilson"],"year":2018,"date_issued":"2018-09-01T07:00:00Z","date_published":"2018-09-01T07:00:00Z","updated_at":"2026-07-24T01:58:39Z","subjects":["Geometry and Topology","almost complex structure","six sphere","rational homotopy theory","de rham homotopy"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://academicworks.cuny.edu/gc_etds/2910","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Dennis Sullivan"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Martin Bendersky","James Simons","Scott Wilson"]},{"key":"dc:creator","label":"Author","values":["Ferlengez, Bora"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-09-08T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The Graduate School and University Center of The City University of New York"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Geometry and Topology","almost complex structure","six sphere","rational homotopy theory","de rham homotopy"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://academicworks.cuny.edu/gc_etds/2910"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In his seminal paper Infinitesimal Computations in Topology, Sullivan constructs algebraic models for spaces and then computes various invariants using them. In this thesis, we use those ideas to obtain a finiteness result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the space of almost complex structures on a manifold. As a special case, we discuss the space of almost complex structures on the six sphere and conclude a conjecture about the ordinary homotopy type of that space.
"]},{"key":"dc:title","label":"Title","values":["Studying the Space of Almost Complex Structures on a Manifold Using de Rham Homotopy Theory"]}]}],"canonical_facts":{"dc:contributor.advisor":["Dennis Sullivan"],"dc:contributor.committeemember":["Martin Bendersky","James Simons","Scott Wilson"],"dc:creator":["Ferlengez, Bora"],"dc:date.available":["2018-09-08T07:00:00Z"],"dc:description.abstract":["In his seminal paper Infinitesimal Computations in Topology, Sullivan constructs algebraic models for spaces and then computes various invariants using them. In this thesis, we use those ideas to obtain a finiteness result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the space of almost complex structures on a manifold. As a special case, we discuss the space of almost complex structures on the six sphere and conclude a conjecture about the ordinary homotopy type of that space.
"],"dc:identifier":["https://academicworks.cuny.edu/gc_etds/2910"],"dc:subject":["Geometry and Topology","almost complex structure","six sphere","rational homotopy theory","de rham homotopy"],"dc:title":["Studying the Space of Almost Complex Structures on a Manifold Using de Rham Homotopy Theory"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Graduate School and University Center of The City University of New York"]},"updated_at":"2026-07-24T01:58:39Z"}