Low dimensional Milnor-Witt stems over R

Abstract

This article computes some motivic stable homotopy groups over R. For 0 <= p - q <= 3, we describe the motivic stable homotopy groups of a completion of the motivic sphere spectrum. These are the first four Milnor-Witt stems. We start with the known Ext groups over C and apply the rho-Bockstein spectral sequence to obtain Ext groups over R. This is the input to an Adams spectral sequence, which collapses in our low dimensional range.

References in corpus (2)

• Motivic Brown-Peterson invariants of the rationals
• Cohomology operations and algebraic geometry

Cited by in corpus (8)

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• Real motivic and $C_2$-equivariant Mahowald invariants
• Topological models for stable motivic invariants of regular number rings
• $\mathbb{R}$-motivic $v_1$-periodic homotopy
• The reduced ring of the $RO(C_2)$-graded $C_2$-equivariant stable stems
• The motivic lambda algebra and motivic Hopf invariant one problem