THE HOMOTOPY GROUPS OF tmf AND OF ITS LOCALIZATIONS
نویسنده
چکیده
(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 ) 2-torsion and 3-torsion, and so its is only at those primes that tmf resembles the sphere spectrum. The 3-primary part of the Hurewitz image is 72-periodic and is given by
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