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BP-cohomology of projective Stiefel manifolds

Part of: Spectral sequences Homology and homotopy of topological groups and related structures Homology and cohomology theories Homotopy theory

Published online by Cambridge University Press:  21 March 2022

Samik Basu  and
Debanil Dasgupta
Samik Basu
Affiliation:
Stat-Math Unit, Indian Statistical Institute, B. T. Road, Kolkata 700108, India ([email protected]; [email protected]; [email protected])
Debanil Dasgupta
Affiliation:
Stat-Math Unit, Indian Statistical Institute, B. T. Road, Kolkata 700108, India ([email protected]; [email protected]; [email protected])
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Abstract

In this paper, we compute the $BP$-cohomology of complex projective Stiefel manifolds. The method involves the homotopy fixed point spectral sequence, and works for complex oriented cohomology theories. We also use these calculations and $BP$-operations to prove new results about equivariant maps between Stiefel manifolds.

Keywords

Stiefel manifoldsBP-cohomologyprojective Stiefel manifoldshomotopy fixed point spectral sequence

MSC classification

Primary: 55N20: Generalized (extraordinary) homology and cohomology theories 57T15: Homology and cohomology of homogeneous spaces of Lie groups
Secondary: 55T25: Generalized cohomology 55P91: Equivariant homotopy theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 2 , April 2023 , pp. 679 - 701
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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