The real-oriented cohomology of infinite stunted projective spaces

Balderrama, William

doi:10.2140/agt.2024.24.4061

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

The real-oriented cohomology of infinite stunted projective spaces

William Balderrama

Algebraic & Geometric Topology 24 (2024) 4061–4084

DOI: 10.2140/agt.2024.24.4061

Abstract

Let $E ℝ$ be an even-periodic real Landweber exact $C_{2}$ –spectrum, and $E R$ be its spectrum of fixed points. We compute the $E R$ –cohomology of the infinite stunted real projective spectra $P_{j}$ . These cohomology groups combine to form the $R O (C_{2})$ –graded coefficient ring of the $C_{2}$ –spectrum

b (E R) = F (E C_{2 +}, i_{*} E R),

which we show is related to $E ℝ$ by a cofiber sequence $Σ^{σ} b (E R) \to b (E R) \to E ℝ$ . We illustrate our description of $π_{⋆} b (E R)$ with the computation of some $E R$ –based Mahowald invariants.

Keywords

real bordism, projective space, Mahowald invariant

Mathematical Subject Classification

Primary: 55N20, 55N22, 55N91, 55Q51

References

Publication

Received: 13 March 2023

Revised: 3 July 2023

Accepted: 29 September 2023

Published: 9 December 2024

Authors

William Balderrama
Department of Mathematics University of Virginia Charlottesville, VA United States

Open Access made possible by participating institutions via Subscribe to Open.

Volume 24, issue 7 (2024)