On algebras and groups of formal series over a small category, non-abelian stochastic cosurfaces and topological quantum field theories - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2020

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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Dates and versions

hal-01961439 , version 1 (19-12-2018)
hal-01961439 , version 2 (12-05-2020)

Identifiers

  • HAL Id : hal-01961439 , version 2

Cite

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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