Topology and Geometry pp 260-314 | Cite as

# Cohomology

Chapter

## Abstract

Let for any permutation

*V*be a vector space over the real numbers. Denote by*A*^{ p }(*V*) the vector space of all alternating multilinear*p*-forms on*V*. That is,*ω*∈*A*^{ p }(*V*) is a function which assigns to each*p*-tuple 〈*X*_{1},…,*X*_{ p }〉 of vectors in*V*, a real number*ω*(*X*_{1},…,*X*_{ p }) such that$$\omega ({X_{\sigma 1}},...,{X_{\sigma p}}) = \operatorname{sgn} (\sigma )\omega ({X_1},...,{X_p})$$

*σ*of 1, 2,…,*p*, and such that*ω*is linear in each variable.## Keywords

Abelian Group Exact Sequence Short Exact Sequence Cochain Complex Injective Resolution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## Copyright information

© Springer Science+Business Media New York 1993