synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
Localization in equivariant de Rham cohomology.
Original articles:
J. J. Duistermaat, G. J. Heckman, On the variation in the cohomology in the symplectic form of the reduced phase space, Invent. Math. 69 (1982) 259-268.
Nicole Berline, Michèle Vergne, Classes caractéristiques équivariantes. Formule de localisation en cohomologie équivariante, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), no. 9, 539–541, MR83m:58002
Michael Atiyah, Raoul Bott, The moment map and equivariant cohomology, Topology 23, 1, 1-28 (1984) (doi:10.1016/0040-9383(84)90021-1)
Victor Guillemin, Shlomo Sternberg, Supersymmetry and equivariant de Rham theory, Springer, 1999.
Victor Guillemin, Shlomo Sternberg, Geometric asymptotics, AMS 1977, online
Review:
Richard Szabo, Equivariant cohomology and localization of path integrals, Lecture Notes in Physics, N.S. Monographs 63. Springer 2000. xii+315 pp. (preprint version: Equivariant localization of path integrals, hep-th/9608068)
Loring Tu, Localization in equivariant cohomology, from biography web on Raoul Bott, node21
Vasily Pestun, Review of localization in geometry (arXiv:1608.02954), chapter in: Vasily Pestun, Maxim Zabzine (eds.) Localization techniques in quantum field theories, J. Phys. A: Math. Theor. 50 440301, 2017 (doi:10.1088/1751-8121/aa63c1, arXiv:1608.02952, full pdf)
Textbook account:
See also:
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