tmf Is Not a Ring Spectrum Quotient of String Bordism
Algebraic Topology
2018-07-03 v4
Abstract
This paper shows that is not a ring spectrum quotient of . In fact, for any prime and any sequence of homogeneous elements of , the -module is not (even abstractly) isomorphic to . It does so by showing that, for any commutative ring spectrum and any sequence of homogeneous elements of , there is an isomorphism of graded -vector spaces where the right-hand side is the rational homology of the (total) Koszul complex of , which is strictly bigger than unless is a -quasi-regular sequence. The result then follows from the fact that the kernel of the -local Witten genus cannot be generated by a -quasi-regular sequence.
Keywords
Cite
@article{arxiv.1312.2440,
title = {tmf Is Not a Ring Spectrum Quotient of String Bordism},
author = {Carl McTague},
journal= {arXiv preprint arXiv:1312.2440},
year = {2018}
}
Comments
9 pages; statement of the new Theorem 3 made clearer