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 $E_2$ 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 The result of this computation is originally due to Hopkins and Mahowald (unpublished).

Publication

Geometry and Topology Monographs **13**: Groups, homotopy and configuration spaces (Tokyo 2005), 2008, pp. 11–40

Date

February, 2008

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