ON THE STEENROD MODULE STRUCTURE OF ℝ-MOTIVIC SPANIER-WHITEHEAD DUALS

Prasit Bhattacharya; Bertrand J. Guillou; Ang Li

doi:10.1090/bproc/227

ON THE STEENROD MODULE STRUCTURE OF ℝ-MOTIVIC SPANIER-WHITEHEAD DUALS

Prasit Bhattacharya, Bertrand J. Guillou, Ang Li

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The ℝ-motivic cohomology of an ℝ -motivic spectrum is a module over the R-motivic Steenrod algebra A^ℝ. In this paper, we describe how to recover the ℝ -motivic cohomology of the Spanier–Whitehead dual DX of an ℝ -motivic finite complex X, as an A^ℝ-module, given the A^ℝ -module structure on the cohomology of X. As an application, we show that 16 out of 128 different A^ℝ-module structures on A^ℝ(1):= 〈Sq¹, Sq²〉 are self-dual.

Original language	English
Pages (from-to)	555-569
Number of pages	15
Journal	Proceedings of the American Mathematical Society, Series B
Volume	11
Issue number	1
DOIs	https://doi.org/10.1090/bproc/227
State	Published - 2024

Bibliographical note

Publisher Copyright:
© 2024 by the author(s).

Funding

Received by the editors October 18, 2023, and, in revised form, April 22, 2024. 2020 Mathematics Subject Classification. Primary 14F42, 55S10. The second author was supported by NSF grant DMS-2003204. The first author was supported by NSF grant DMS-2305016.

Funders	Funder number
National Science Foundation Arctic Social Science Program	DMS-2003204, DMS-2305016

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

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abstract = "The ℝ-motivic cohomology of an ℝ -motivic spectrum is a module over the R-motivic Steenrod algebra Aℝ. In this paper, we describe how to recover the ℝ -motivic cohomology of the Spanier–Whitehead dual DX of an ℝ -motivic finite complex X, as an Aℝ-module, given the Aℝ -module structure on the cohomology of X. As an application, we show that 16 out of 128 different Aℝ-module structures on Aℝ(1):= 〈Sq1, Sq2〉 are self-dual.",

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ON THE STEENROD MODULE STRUCTURE OF ℝ-MOTIVIC SPANIER-WHITEHEAD DUALS

Abstract

Bibliographical note

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ASJC Scopus subject areas

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