Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Projective resolutions and Poincaré duality complexes

Authors: D. J. Benson and Jon F. Carlson
Journal: Trans. Amer. Math. Soc. 342 (1994), 447-488
MSC: Primary 20J06; Secondary 18G40
MathSciNet review: 1142778
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let k be a field lof characteristic $ p > 0$ and let G be a finite group. We investigate the structure of the cohomology ring $ {H^\ast}(G,k)$ in relation to certain spectral sequences determined by systems of homogeneous parameters for the cohomology ring. Each system of homogeneous parameters is associated to a complex of projective kG-modules which is homotopically equivalent to a Poincaré duality complex. The initial differentials in the hypercohomology spectral sequence of the complex are multiplications by the parameters, while the higher differentials are matric Massey products. If the cohomology ring is Cohen-Macaulay, then the duality of the complex assures that the Poincaré series for the cohomology satisfies a certain functional equation. The structure of the complex also implies the existence of cohomology classes which are in relatively large degrees but are not in the ideal generated by the parameters. We consider several other questions concerned with the minimal projective resolutions and the convergence of the spectral sequence.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20J06, 18G40

Retrieve articles in all journals with MSC: 20J06, 18G40

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society