Year: 2023
Type: preprint
Abstract: The $\mathbb{R}$-motivic cohomology of an $\mathbb{R}$-motivic spectrum is a module over the $\mathbb{R}$-motivic Steenrod algebra $\mathcal{A}^{\mathbb{R}}$. In this paper, we describe how to recover the $\mathbb{R}$-motivic cohomology of the Spanier-Whitehead dual $\mathrm{DX}$ of an $\mathbb{R}$-motivic finite complex $\mathrm{X}$, as an $\mathcal{A}^{\mathbb{R}}$-module, given the $\mathcal{A}^{\mathbb{R}}$-module structure on the cohomology of $\mathrm{X}$. As an application, we show that 16 out of 128 different $\mathcal{A}^{\mathbb{R}}$-module structures on $\mathcal{A}^{\mathbb{R}}(1):= \langle \mathrm{Sq}^1, \mathrm{Sq}^2 \rangle$ are self-dual.
Source: arXiv (Cornell University)
Institution: New Mexico State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4387210550