Holmstrom Locally finite homology

Locally finite homology

Carlsson in K-theory handbook, page 28.

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Locally finite homology

Locally compact topological spaces (Carlsson)


Locally finite homology

Defined similarly to ordinary homology, but with the the defining chain complexes taken to be “locally finite”. The resulting homology groups are functorial with respect to proper continuous maps, and proper homotopy invariant. It is formally dual to Cohomology with compact supports. It agrees with ordinary homology on compact spaces.

Example: For n\mathbb{R}^n, the only nontrivial group sits in degree nn.

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Locally finite homology

Carlsson claims, without going into details, that one can adapt the classical use of spectra to interpret locally finite homology as a representable functor.


Locally finite homology

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Locally finite homology

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Created on June 10, 2014 at 21:14:54 by Andreas Holmström