In algebraic topology, several types of products are defined on homological and cohomological theories.
The cross product edit
The cap product edit
The slant product edit
The cup product edit
This product can be understood as induced by the exterior product of differential forms in de Rham cohomology. It makes the singular cohomology of a connected manifold into a unitary supercommutative ring.
See also edit
- Singular homology
- Differential graded algebra: the algebraic structure arising on the cochain level for the cup product
- Poincaré duality: swaps some of these
- Intersection theory: for a similar theory in algebraic geometry
References edit
- Hatcher, A., Algebraic Topology, Cambridge University Press (2002) ISBN 0-521-79540-0, especially chapter 3.