On the Tate spectrum of tmf at the prime 2

Details On the Tate spectrum of tmf at the prime 2 On the Tate spectrum of tmf at the prime 2

2009-04-23

arxiv.org/abs/0904.3687v1

Mathematics

Algebraic Topology

23 pages, 10 figures

Scientific paper

Computations involving the so-called 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 lending further credence toward its truth. The root invariant is closely related to Mahowald's inverse limit construction of the Tate spectrum. Computations have shown the Tate spectrum of v_n-periodic cohomology theories are v_n-torsion. The purpose of this paper is to split the Tate spectrum of tmf as a wedge of suspensions of bo, providing yet another example to the literature.

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