Supriya Ghosh (Editor)

Products in algebraic topology

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In algebraic topology, several types of products are defined on homological and cohomological theories.

Contents

The cross product

H p ( X ) ⊗ H q ( Y ) → H p + q ( X × Y )

The cap product

⌢   : H p ( X ; R ) × H q ( X ; R ) → H p − q ( X ; R )

The slant product

∖   : H p ( X ; R ) × H q ( X × Y ; R ) → H q − p ( Y ; R )

The cup product

H p ( X ) ⊗ H q ( X ) → H p + q ( X )

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.

References

Products in algebraic topology Wikipedia
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