Topological André-Quillen homology for commutative
S-algebras was introduced by Basterra following work of Kriz, and has been intensively studied by several authors. In this
paper we discuss it as a homology theory on CW commutative
S-algebras and apply it to obtain results on minimal atomic
p-local
S-algebras which generalise those of Baker and May for
p-local spectra and simply connected spaces. We exhibit some new examples of minimal atomic commutative
S-algebras.
Keywords
S-module -
S-algebra - Cell algebra - Topological André-Quillen (co)homology
Mathematics Subject Classification (2000) 55P43 - 13D03 - 55N35 - 55P48
Communicated by B. Richter.
A. Baker was partially supported by a YFF Norwegian Research Council grant while at the University of Oslo in 2007–8, a Carnegie
Trust for the Universities of Scotland grant, and Intas grants 03-51-3251 and 06-1000017-8609.
H. Gilmour was supported by an EPSRC studentship.
P. Reinhard was supported by an ORS grant.
We would like to thank M. Basterra, P. Kropholler, M. Mandell, P. May, B. Richter, J. Rognes and S. Sagave for numerous helpful
comments. We are also very grateful to the referee for encouraging us to rethink significantly issues of notation and structure,
thus improving the structure of the paper.