A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold
type: Item
instance of: scholarly article
title: A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold
zbMATH Open document ID: 0822.60057
DOI: 10.1016/0393-0440(94)00023-W
published in: Journal of Geometry and Physics
publication date: 1995-09-20T00:00:00Z
review text: This dense and difficult paper deals with the set \(H_ g\) of paths \(\gamma : [0,1] \to M\) (a compact manifold) such that \(\gamma(1) = g \cdot \gamma(0)\) (\(g\) being one isometry of \(M\)), endowed with its Wiener-like measure \(Y_ g\) (for which integration by parts is established); a diffusion process \(w_ t\) is defined on \((H_ g, Y_ g)\) via a Dirichlet form, and is shown to verify an exponential localisation property for \(t \downarrow 0\). Then a differential calculus for \(n\)-forms and a regularised version of the de Rham-Hodge-Kodaira operator on \(H_ g\) are defined, and a semiclassical approximation of this operator is performed, such that the index of the limit operator equals the ``orbit Euler characteristic'' of physicists.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 20P05
Mathematics Subject Classification ID: 81T30
zbMATH DE Number: 763310
zbMATH Keywords: stochastic analysis
zbMATH Keywords: loop groups
zbMATH Keywords: de Rham operator
zbMATH Keywords: Euler number
zbMATH Keywords: orbifold
author: Rémi Léandre
author: Shi-Shyr Roan
MaRDI profile type: Publication
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full work available at URL: 0393-0440(94)00023-w
OpenAlex ID: W2049401175
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