Advertisement

Borel Moore Homology

  • Birger Iversen
Chapter
  • 1.9k Downloads
Part of the Universitext book series (UTX)

Abstract

Throughout this section we consider a commutative no- etherian ring k and let K* denote an injective resolution of k in the category of k-modules. For a complex C* of k-modules we put
$$ {\text{D}}{{{\text{C}}}^{*}} = {\text{HO}}{{{\text{M}}}_{{\text{k}}}}^{*}({{{\text{C}}}^{*}},{{{\text{K}}}^{*}}) $$
For a locally compact space X we define
$$ {{{\text{H}}}_{{\text{i}}}}({\text{X}},{\text{k}}) = {{{\text{H}}}^{{{\text{ - i}}}}}{\text{D}}{{{\text{R}}}^{*}}{{\Gamma }_{{\text{C}}}}({\text{X}},{\text{k}})\qquad ;{\text{i}}\epsilon \mathbb{Z} $$
(1.1)
the i’th Borel-Moore homology group with coefficients in k.

Keywords

Compact Space Short Exact Sequence Projection Formula Injective Resolution Commutative Noetherian Ring 
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.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Birger Iversen
    • 1
  1. 1.Mathematisk InstitutAarhus UniversitetAarhus CDenmark

Personalised recommendations