92-169 Rogers Alice

Stochastic Calculus in Superspace II: Differential forms, supermanifolds and the Atiyah-Singer index theorem (58K, TeX) Oct 26, 92

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Abstract. Starting with vector bundles over manifolds, supermanifolds are constructed whose function algebras correspond to twisted differential forms. Stochastic calculus for bosonic and fermionic Brownian paths is used to provide a geometric construction of Brownian paths on these supermanifolds. A Feynman-Kac formula for the heat kernel of the Laplace-Beltrami operator is then derived. This is used to provide a simple, rigorous version of the supersymmetric proofs of the Atiyah-Singer index theorem.

Files: 92-169.tex