@MISC{Hovey91spinbordism, author = {Mark A. Hovey}, title = {Spin Bordism and Elliptic Homology}, year = {1991} }
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Abstract
In an attempt to understand elliptic homology at the prime 2, Ochanine [Och] introduced a genus fi q : MSpin ! B, where B is a ring which is isomorphic to Z[ 1 2 ][ffi; ffl] upon inverting 2. He asked whether MSpin (X)\Omega MSpin B[ffl \Gamma1 ] is a homology theory. However, Kreck and Stolz [KS] have recently shown that this is false. They construct a geometric homology theory whose coefficient ring is B[ffl \Gamma1 ]. Let v be an element of B corresponding to 64(ffi 2 \Gamma ffl). We show, using the work of Kreck and Stolz and previous work of Hopkins and the author [HH], that MSpin (X)\Omega MSpin B[v \Gamma1 ] is a homology theory, in fact one of the theories introduced by Kreck and Stolz. 1 Introduction Elliptic homology, introduced by Landweber, Ravenel, and Stong [LRS], seems to tie together algebraic topology, modular forms, and part of modern physics. See, for example, Witten's papers [Witten 1], [Witten 2]. However, the subject is still in its infancy...