Transchromatic extensions in motivic and Real bordism

2020/05/21 by Beaudry, Agnes, Hill, Michael A., Shi, XiaoLin Danny +1 · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.10888

Abstract

We show a number of Toda brackets in the homotopy of the motivic bordism spectrum MGL and of the Real bordism spectrum MU_{\mathbb R}. These brackets are "red-shifting" in the sense that while the terms in the bracket will be of some chromatic height n, the bracket itself will be of chromatic height (n+1). Using these, we deduce a family of exotic multiplications in the π_(∗,∗)MGL-module structure of the motivic Morava K-theories, including non-trivial multiplications by 2. These in turn imply the analogous family of exotic multiplications in the π_⋆MU_\mathbb R-module structure on the Real Morava K-theories.

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