Transchromatic extensions in motivic and Real bordism
Agnes Beaudry, Michael A. Hill, XiaoLin Danny Shi, Mingcong Zeng

TL;DR
This paper explores chromatic height shifts in motivic and Real bordism spectra via Toda brackets, revealing exotic multiplications and non-trivial elements in their homotopy groups.
Contribution
It introduces red-shifting Toda brackets in motivic and Real bordism spectra, leading to new exotic multiplications in their homotopy modules.
Findings
Identification of red-shifting Toda brackets in $MGL$ and $MU_{\mathbb R}$
Discovery of exotic multiplications including non-trivial 2-multiplications
Implications for the structure of motivic and Real Morava K-theories
Abstract
We show a number of Toda brackets in the homotopy of the motivic bordism spectrum and of the Real bordism spectrum . These brackets are "red-shifting" in the sense that while the terms in the bracket will be of some chromatic height , the bracket itself will be of chromatic height . Using these, we deduce a family of exotic multiplications in the -module structure of the motivic Morava -theories, including non-trivial multiplications by . These in turn imply the analogous family of exotic multiplications in the -module structure on the Real Morava -theories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds · Advanced Topics in Algebra
