Resolutions modeled on ternary trees

Christopher W. Stark

Vol. 173 (1996), No. 2, 557–569

DOI: 10.2140/pjm.1996.173.557

Abstract

Let Γ be a discrete group. An extension of Swan’s classic technique of grafting chain complexes shows that Γ is of type FP(∞) if and only if there is an augmented chain complex C_∗ of finitely generated projective ZΓ-modules such that each H_i(C) is finitely generated over Z.

Mathematical Subject Classification 2000

Primary: 57M07

Secondary: 20J05, 55U15

Milestones

Received: 19 September 1993

Published: 1 April 1996