The Steenrod algebra has to do with the cohomology operations in singular cohomology with integer mod 2 coefficients. For every and there are natural transformations of functors (1) satisfying: ...
When two cycles have a transversal intersection on a smooth manifold , then is a cycle. Moreover, the homology class that represents depends only on the homology class of and . The sign of is determined by the orientations...
A homology class in a singular homology theory is represented by a finite linear combination of geometric subobjects with zero boundary. Such a linear combination is considered to be homologous to zero if it is the boundary of...
Homology is a concept that is used in many branches of algebra and topology. Historically, the term "homology" was first used in a topological sense by Poincaré. To him, it meant pretty much what is now called a bordism,...
The homomorphism which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism is defined by (2) ...
