In algebraic topology, several types of products are defined on homological and cohomological theories.
The cross product
The cap product
The slant product
The cup product
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
- 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
- Hatcher, A., Algebraic Topology, Cambridge University Press (2002) ISBN 0-521-79540-0, especially chapter 3.