Studying the Space of Almost Complex Structures on a Manifold Using de Rham Homotopy Theory

<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>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The Graduate School and University Center of The City University of New York

Year dc:date.available

2018

Author dc:creator

• Ferlengez, Bora

Advisor dc:contributor.advisor

• Dennis Sullivan

Committee members dc:contributor.committeemember

• Martin Bendersky
• James Simons
• Scott Wilson

• Geometry and Topology
• almost complex structure
• six sphere
• rational homotopy theory
• de rham homotopy

Repository record dc:identifier

https://academicworks.cuny.edu/gc_etds/2910

OAI identifier oai:identifier

oai:academicworks.cuny.edu:gc_etds-3931