On homology of the MSU spectrum

2021/08/28 by Semyon Abramyan, Abramyan, Semyon
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2108.12713

Abstract

We give a complete proof the Novikov isomorphism \varOmega^SU⊗ \mathbb Z[\textstyle\frac12]≅\mathbb Z[\textstyle\frac12][y₂,y₃,…],\quaddeg y_i=2i, where \varOmega^SU is the SU-bordism ring. The proof uses the Adams spectral sequence and a description of the comodule structure of H_*(MSU; \mathbb F_p) over the dual Steenrod algebra \mathfrak A_p^* with odd prime p, which was also missing in the literature.

Related

• The homology of tmf
• The Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres
• The algebraic Novikov spectral sequence for topological modular forms
• The motivic Adams-Novikov spectral sequence at odd primes over ℂ and ℝ
• The \mathbb C-motivic Adams-Novikov spectral sequence for topological modular forms