Stochastic cohomology of Chen-Souriau and line bundle over the Brownian bridge

• 成果类型: Article
• 署名作者: Léandre, R
• 署名单位: Universite de Lorraine
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/PL00008779
• 发表日期: 2001
• 页码: 168-182
• 关键词: hodge-kodaira decomposition; string structures

摘要

We define a stochastic cohomology theory related to a stochastic diffeology for the Hoelder loop space. We show that the stochastic de Rham cohomology groups are equal to the deterministic de Rham cohomology groups of the Hoelder loop space. As an application, we show that a stochastic line bundle over the Brownian bridge (with fiber almost surely defined) is isomorphic to a true line bundle over the Hoelder loop space.