Special It\^o maps and an $L^2$ Hodge theory for one forms on path spaces

K. D. Elworthy; Xue-Mei Li

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arXiv · 1911.09618

Special It\^o maps and an $L^2$ Hodge theory for one forms on path spaces

K. D. Elworthy·Xue-Mei Li

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Abstract

We prove a Kodaira-Hodge decomposition on differential 1-forms on the space of non-smooth paths over a Riemannian manifold, allowing us to define the corresponding first cohomology group. This uses the It\^o map of a Brownian system and damped stochastic parallel translation.

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BibTeX RIS

K. D. Elworthy, Xue-Mei Li. 2019-11-21. Special It\^o maps and an $L^2$ Hodge theory for one forms on path spaces. https://arxiv.org/abs/1911.09618

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