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Mathematische Zeitschrift

, Volume 291, Issue 3–4, pp 821–829 | Cite as

On the Tate spectrum of \(\mathrm {tmf}\) at the prime 2

  • Scott M. BaileyEmail author
  • Nicolas Ricka
Article
  • 21 Downloads

Abstract

Computations involving the Mahowald invariant prompted Mahowald and Shick to develop the slogan: “the Mahowald invariant of \(v_n\)-periodic homotopy is \(v_n\)-torsion”. While neither a proof, nor a precise statement, of this slogan appears in the literature, numerous authors have offered computational evidence in support of its fundamental idea. The Mahowald invariant is closely related to his inverse limit description of the Tate spectrum, and computations have shown the Tate spectrum of \(v_n\)-periodic cohomology theories to be \(v_n\)-torsion. The purpose of this paper is to split the Tate spectrum of \(\mathrm {tmf}\) as a wedge of suspensions of \(\mathrm {ko}\), providing yet another example in support of the slogan to the existing literature.

Keywords

Topological modular forms Tate spectrum Mahowald invariant 

Mathematics Subject Classification

55P42 55T15 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsClayton State UniversityMorrowUSA
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA

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