|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Equivariant cohomology
of projective spaces
Samik Basu, Pinka Dey and Aparajita Karmakar |
|
Algebraic & Geometric Topology 25 (2025) 3049–3088
|
 |
Abstract |
|
We compute the equivariant homology and cohomology of projective spaces with integer coefficients. More precisely, in the case of cyclic groups, we show that the cellular filtration of the projective space of lines inside copies of the regular representation yields a splitting of as a wedge of suspensions of . This is carried out both in the complex case, and also in the quaternionic case, and further, for the -action on by complex conjugation. We also observe that these decompositions imply a degeneration of the slice tower in these cases. Finally, we describe the cohomology of the projective spaces when is of prime power order, with explicit formulas for -coefficients. Letting , this also describes the equivariant homology and cohomology of the classifying spaces of and . |
Keywords
projective spaces, equivariant classifying spaces,
equivariant homotopy, equivariant homology
|
Mathematical Subject Classification
Primary: 55N91, 57S17
Secondary: 55P91
|
References |
Publication
Received: 21 March 2024
Revised: 11 June 2024
Accepted: 1 August 2024
Published: 17 September 2025
|
Authors |
| Samik Basu | |
| Stat-Math Unit Indian Statistical Institute Kolkata India |
|
| Pinka Dey | |
| Department of Mathematics National Institute of Calicut Kerala India |
|
| Aparajita Karmakar | |
| Department of Mathematics IIT Bombay Mumbai India |
|
| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
