Subject: Question about Toda's Z_p-spaces From: "Douglas C. Ravenel" Date: Thu, 2 Nov 2006 18:11:54 -0500 (EST) Dear Topologists, In Toda's 1971 paper "Algebra of stable homotpy of Z_p-spaces and applications," he defines a derivation \theta on the graded group of maps from one Z_p-space (or module spectrum over the mod p Moore spectrum) to another, and proves (Theorem 2.2) \theta(\gamma \gamma') = \theta(\gamma)\gamma' +(-1)^{deg \gamma}\gamma\theta(\gamma') I do not see how this degree is well defined. He has Z_p-spaces W, X and Y with maps \gamma':\Sigma^{i+j}W \to \Sigma^j X and \gamma :\Sigma^j X \to Y, which means that the degree of \gamma is j. But suppose X=\Sigma X' and we rewrite the maps as \gamma':\Sigma^{i+j}W \to \Sigma^{j+1} X' and \gamma :\Sigma^{j+1}X' \to Y, so now the degree of \gamma is j+1 and the formula above gives a different answer. What am I missing here? Doug Douglas C. Ravenel Department of Mathematics |819 Hylan Building University of Rochester |(585) 275-4415 Rochester, New York 14627 |FAX (585) 273-4655 Email: doug@math.removethis.rochester.&this.edu Personal home page: http://www.math.rochester.edu/people/faculty/doug/