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 special kind of Poincaré duality space: a CW-complex which satisfies Poincaré duality and in this respect thus behaves like a closed manifold. Also called a homology manifold, therefore.
C. T. C. Wall, Poincaré complexes I, Annals of Mathematics, Second Series, Volume 86 (1967) pdf
)
Andrew Ranicki, 45 slides on chain duality, September 1996 (pdf)
With an eye towards generalization in spectral geometry (spectral triples):
Last revised on March 20, 2014 at 07:53:56. See the history of this page for a list of all contributions to it.