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Witten Laplacian and Twisted de Rham Cohomology (Integral representations and twisted cohomology in the theory of differential equations)

Katsunori Iwasaki

Abstract

This paper presents asurvey of arecent work by the author on an intersection theory for twisted de Rham cohomology and its ap- plications to special function theory.While Witten used atwisted Laplacian, twisted by aMorse function, to develop his Morse theory as asuper-symmetric quantum mechanics, we use atwisted Laplacian, twisted by an isolated singularity, in aquite different situation.

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Key concepts: De Rham cohomology, Mathematics, Chern–Weil homomorphism, Cohomology, Pure mathematics, Hodge theory, Differential form, Čech cohomology