Products in algebraic topology
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.