Contents

duality

# Contents

## Definition

###### Definition

A topological space for which there is $d \in \mathbb{N}$ and a class $[X] \in H_d(X)$ such that the cap product induces isomorphisms

$(-) \cap [X] \;\colon\; H^\bullet(X) \stackrel{\simeq}{\to} H_{d-\bullet}(X)$

between ordinary cohomology and ordinary homology groups as indicated, is called a Poincaré duality space.

If $X$ is moreover a CW-complex then this it is sometimes called a Poincaré complex or even Poincaré manifold.

See at Poincaré duality for more.

## References

In the general concext of spectral geometry (spectral triples):

• Alain Connes, page 10 of Noncommutative geometry and reality, J. Math. Phys. 36 (11), 1995 (pdf)

Last revised on March 20, 2014 at 07:57:05. See the history of this page for a list of all contributions to it.