J Austral Math Soc Ser A 49 pp364--385, 1990.

Stably Free Resolutions of Lattices Over Finite Groups

K. W. Gruenberg

Abstract

For a ZG-lattice A, the nth partial free Euler characteristic e_n(A) is defined as the infimum of all

n å i=0  (-1)n-idG(Fi)

where F_* varies over all free resolutions of A. It is shown that there exists a stably free resolution of E_* of A which realises e_n(A) for all n ³ 0 and that the function n ® e_n(A) is ultimately polynomial on residue classes. The existence of E_* is established with the help of new invariants s_n(A) of A. These are elements in certain image groups of the projective class group of ZG. When ZG allows cancellation, E_* is ultimately periodic of period a multiple of the projective period of A.

1980 AMS Subject Classification (1985 Revision): 20C10, 20C05, 18G10

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Authors

K. W. Gruenberg

Queen Mary and Westfield College, London, England.