The Zero Slice of Quaternionic Real Bordism
Bertrand J. Guillou, Jesse Keyes, and David Mehrle

TL;DR
This paper computes the zero slice of a quaternionic MU spectrum constructed via the Hill-Hopkins-Ravenel norm, advancing the understanding of its slice spectral sequence and homotopy Mackey functors.
Contribution
It introduces the computation of the zero slice and a subring of homotopy Mackey functors for the quaternionic MU spectrum using the Hill-Hopkins-Ravenel norm.
Findings
Computed the zero slice of the $Q_8$-spectrum $N_{C_2}^{Q_8} ext{MU} ext{R}$.
Identified a bigraded subring of the RO($Q_8$)-graded homotopy Mackey functors.
Progressed towards the full computation of the slice spectral sequence for this spectrum.
Abstract
Using the Hill-Hopkins-Ravenel norm, one can produce a -spectrum , where is the quaternion group. Working towards a computation of the slice spectral sequence for , we compute the zero slice of and a bigraded subring of the -graded homotopy Mackey functors of this slice.
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