BibTeX
@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...
Keyphrases
elliptic homology spin bordism homology theory introduction elliptic homology coefficient ring omega mspin ffl gamma1 stong lr geometric homology theory modern physic author hh ochanine och gamma ffl algebraic topology previous work genus fi ffl gamma1 modular form stolz k omega mspin gamma1
