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$mathit{tmf}$-based Mahowald invariants

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 نشر من قبل J.D. Quigley
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English
 تأليف J.D. Quigley




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The $2$-primary homotopy $beta$-family, defined as the collection of Mahowald invariants of Mahowald invariants of $2^i$, $i geq 1$, is an infinite collection of periodic elements in the stable homotopy groups of spheres. In this paper, we calculate $mathit{tmf}$-based approximations to this family. Our calculations combine an analysis of the Atiyah-Hirzebruch spectral sequence for the Tate construction of $mathit{tmf}$ with trivial $C_2$-action and Behrens filtered Mahowald invariant machinery.



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