On the nonexistence of Smith-Toda complexes
Algebraic Topology
2007-05-23 v1
Abstract
Let p be a prime. The Smith-Toda complex V(k) is a finite spectrum whose BP-homology is isomorphic to BP_*/(p,v_1,...,v_k). For example, V(-1) is the sphere spectrum and V(0) the mod p Moore spectrum. In this paper we show that if p > 5, then V((p+3)/2) does not exist and V((p+1)/2), if it exists, is not a ring spectrum. The proof uses the new homotopy fixed point spectral sequences of Hopkins and Miller.
Keywords
Cite
@article{arxiv.math/9810178,
title = {On the nonexistence of Smith-Toda complexes},
author = {Lee S. Nave},
journal= {arXiv preprint arXiv:math/9810178},
year = {2007}
}
Comments
10 pages, AMSLateX