homology theory


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homology theory

[hə′mäl·ə·jē ‚thē·ə·rē]
(mathematics)
Theory attempting to compare topological spaces and investigate their structures by determining the algebraic nature and interrelationships appearing in the various homology groups.
References in periodicals archive ?
Putnam defines a type of homology theory for Smale spaces, which include the basic sets for Smale's Axiom A diffeomorphism.
One thing is to use category theory in order to construct a unified homology theory like Eilenberg and Steenrod did in their book, or introduce schemes and the etale cohomology as Grothendieck did for the purpose of finding suitable invariants for algebraic varieties over finite fields and in order to prove the Weil conjectures.
An introduction to intersection homology theory, 2d ed.