Diffeological Generalized Formal Series: An Overview

2025/08/06 by Magnot, Jean-Pierre
#13F05 #18F40 #58A05 #FOS: Mathematics #History and Overview (math.HO)

paper · doi:10.48550/arxiv.2508.15786

Abstract

We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in mathematical physics, particularly in contexts where standard atlases and charts are insufficient. Applications to tensor structures and categorical gradings are discussed, and emerging applications are mentioned.

Citations

• Kadomtsev-Petviashvili hierarchies with non-formal pseudo-differential operators, non-formal solutions, and a Yang-Mills--like formulation
• On diffeologies from infinite dimensional geometry to PDE constrained optimization
• Diffeological, Frölicher, and Differential Spaces
• Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase\n factorization, and Fr "olicher Lie groups
• Mackey-complete spaces and power series -- A topological model of Differential Linear Logic
• Diffeologies, Differential Spaces, and Symplectic Geometry

Related

• Groupoids in Diffeology
• Topology and geometry of the general composition of formal power series -- towards Fréchet-Lie group-like formalism
• Why Diffeology?
• Formal conjugacy and asymptotic differential algebra
• Characterizations of Some Class of Formal Power Series via MÖbius Categories of Full Binomial Type