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Explicit homotopy equivalences in dimension two

Published online by Cambridge University Press:  06 November 2002

F. E. A. JOHNSON
F. E. A. JOHNSON
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT. e-mail: [email protected]
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Abstract

Let G be a finite group; by an algebraic 2-complex over G we mean an exact sequence of Z[G]-modules of the form:

E = (0 → J → E2 → E1 → E0 → Z → 0)

where Er is finitely generated free over Z[G] for 0 [les ] r [les ] 2. The module J is determined up to stability by the fact of appearing in such an exact sequence; we denote its stable class by Ω3(Z); E is said to be minimal when rkZ(J) attains the minimum possible value within Ω3(Z).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 3 , November 2002 , pp. 411 - 430
Copyright
© 2002 Cambridge Philosophical Society

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