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- W2077854514 abstract "Abstract In his famous paper (Witten E. Super-symmetry and Morse Theory. J Diff Geom 1982; 17:661–692), Witten used a twisted Laplacian, twisted by a Morse function, to develop his Morse theory as a super-symmetric quantum mechanics. Afterwards, in their studies on puits multiples en mecanique semi-classique, Helffer and Sjöstrand (Helffer B, Sjöstrand J. Puits Multiples en Mecanique Semi-classique IV, Etude du Complexe de Witten. Comm. Partial Differential Equations 1985; 10:245–340) made a detailed investigation of Witten's complexes. In this paper, we use a twisted Laplacian, twisted by a versal deformation of an isolated singularity (invariant under a finite unitary reflection group), to construct a duality between a pair of polynomial twisted de Rham cohomology groups associated with the isolated singularity. The construction is based on a twisted version of Hodge-Kodaira decomposition derived through a pseudo-differential calculus of Witten's twisted Laplacian. Discussion is also made on the real structure and super-symmetry, compatible with the duality constructed, of the twisted de Rham cohomology." @default.
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- W2077854514 date "2003-01-06" @default.
- W2077854514 modified "2023-09-23" @default.
- W2077854514 title "Isolated Singularity, Witten's Laplacian, and Duality for Twisted de Rham Cohomology" @default.
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- W2077854514 doi "https://doi.org/10.1081/pde-120019373" @default.
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