On the Tate spectrum of tmf at the prime 2

2009/04/23 by S. M. Bailey, Bailey, Scott M., Nicolas Ricka +1
Mathematics · Physics and Astronomy · #55P42 #55T15 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0904.3687

openalex publication_date 2009/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Computations involving the root invariant prompted Mahowald and Shick to develop the slogan: "the root 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 root invariant is closely related to Mahowald's 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 tmf as a wedge of suspensions of kO, providing yet another example in support of the slogan to the existing literature.

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