Homotopical computations for projective Stiefel manifolds and related quotients

Date of Submission

2-1-2024

Date of Award

10-1-2024

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Mathematics

Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

Supervisor

Basu, Samik (TSMU-Kolkata)

Abstract (Summary of the Work)

It deals with various homogeneous spaces associated with the real and complex Stiefel manifolds and their homotopical computations. Primarily we work with the complex projective Stiefel manifolds. We compute their Brown-Peterson cohomology using homotopy fixed point spectral sequence and then using BP-cohomology operations provide some criteria for non-existence of an equivariant map between various complex projective Stiefel manifolds under the action of the circle group. We also study the p-local homotopy type of complex projective Stiefel manifolds and various other quotients of Stiefel manifolds and show that they admit a product decomposition into a complex projective space or lens space and some bunch of odd dimensional spheres after p-localization for all but finitely many primes p. We also calculate characteristic classes for certain quotients of Stiefel manifolds and then derive results on certain numerical invariants, such as characteristic rank, skew embedding dimensions for those spaces

Comments

ProQuest Collection ID: https://www.proquest.com/pqdtlocal1010185/dissertations/fromDatabasesLayer?accountid=27563

Control Number

ISILib-TH

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DSpace Identifier

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

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