COMPUTATION OF THE HOMOTOPY OF THE SPECTRUM tmf
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چکیده
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 The result of this computation is originally due to Hopkins and Mahowald (unpublished).
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(1) π∗(S) −→ π∗(tmf ) −→ MF∗ that we now describe. Both maps are surprisingly close to being isomorphisms (even though π∗(S) and MF∗ have nothing to do with each other). The first map (1) is the Hurewitz homomorphism: being a ring spectrum, tmf admits a unit map from the sphere spectrum S. This induces a map in homotopy π∗(S) → π∗(tmf ), which is an isomorphism on π0. The only torsion in π∗(tmf...
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تاریخ انتشار 2004