On the nonexistence of Smith-Toda complexes

Details On the nonexistence of Smith-Toda complexes On the nonexistence of Smith-Toda complexes

1998-10-30

arxiv.org/abs/math/9810178v1

Mathematics

Algebraic Topology

10 pages, AMSLateX

Scientific paper

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.

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