Balance with Unbounded Complexes

Authors

Edgar E. Enochs, University of KentuckyFollow
Sergio Estrada, Universidad de MurciaFollow
Alina Iacob, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

6-2012

Publication Title

Bulletin of the London Mathematical Society

DOI

10.1112/blms/bdr101

ISSN

1469-2120

Abstract

Given a double complex X there are spectral sequences with the E₂ terms being either H_I (H_II(X)) or H_II(H_I(X)). But if H_I(X)=H_II(X)=0, then both spectral sequences have all their terms 0. This can happen even though there is nonzero (co)homology of interest associated with X. This is frequently the case when dealing with Tate (co)homology. So, in this situation the spectral sequences may not give any information about the (co)homology of interest. In this article, we give a different way of constructing homology groups of X when H_I(X)=H_II(X)=0. With this result, we give a new and elementary proof of balance of Tate homology and cohomology.

Comments

This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the author must have permission to distribute the work or the work must be available under the Creative Commons Attribution license, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Bulletin of the London Mathematical Society.

Recommended Citation

Iacob A, E.E. Enochs, S. Estrada. “Balance with Unbounded Complexes”, Bulletin of the London Mathematical Society, 44(3): 439-442, 2012. doi:10.1112/blms/bdr101