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On algebras and groups of formal series over a small category, non-abelian stochastic cosurfaces and topological quantum field theories

Abstract : Based on the example of stochastic cosurfaces, we develop the notion of groups of series indexed by a graded small category, with coefficients in a Fr\"olicher algebra. The presence of the notion of small category is motivated by the cobordism-like relations of stochastic cosurfaces, while the use of Fr\"olicher algebra is a framework adapted to convolution of probabilities. Basic description of these groups, which generalize classical groups of series, is given, and the example raised by non-abelian stochatic cosurfaces of any dimension is studied.MSC(2010): 22E65, 22E66, 58B25, 70G65.
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https://hal.archives-ouvertes.fr/hal-01961439
Contributor : Jean-Pierre Magnot <>
Submitted on : Tuesday, May 12, 2020 - 9:32:09 AM
Last modification on : Friday, May 15, 2020 - 2:30:36 AM

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Jean-Pierre Magnot. On algebras and groups of formal series over a small category, non-abelian stochastic cosurfaces and topological quantum field theories. 2020. ⟨hal-01961439v2⟩

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