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Computation of the homotopy of the spectrum tmf
Tilman Bauer
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Geometry & Topology Monographs 13
(2008) 11–40
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Abstract
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This paper contains a complete computation of the homotopy ring of the
spectrum of topological modular forms constructed by Hopkins and
Miller. The computation is done away from 6, and at the
(interesting) primes 2 and 3 separately, and in each of the latter
two cases, a sequence of algebraic Bockstein spectral sequences is
used to compute the E2 term of the elliptic Adams–Novikov spectral
sequence from the elliptic curve Hopf algebroid. In a further step,
all the differentials in the latter spectral sequence are
determined. The result of this computation is originally due to
Hopkins and Mahowald (unpublished).
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Keywords
topological modular forms, elliptic
cohomology, Adams–Novikov spectral sequence
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Mathematical Subject Classification
Primary: 55N34
Secondary: 55T15
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Publication
Received: 30 September 2005
Revised: 1 September 2006
Accepted: 11 October 2006
Published: 22 February 2008
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