abstract duality: opposite category,
concrete duality: dual object, dualizable object, fully dualizable object, dualizing object
Examples
between higher geometry/higher algebra
Langlands duality, geometric Langlands duality, quantum geometric Langlands duality
In QFT and String theory
Riemann integration, Lebesgue integration
line integral/contour integration
integration of differential forms
integration over supermanifolds, Berezin integral, fermionic path integral
Kontsevich integral, Selberg integral, elliptic Selberg integral
integration in ordinary differential cohomology
integration in differential K-theory
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
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.
In the general concext of spectral geometry (spectral triples):
Last revised on August 14, 2023 at 18:37:23. See the history of this page for a list of all contributions to it.