Differential Geometry of Microlinear Frolicher Spaces II

zbMATH Open1270.58001arXiv1003.4317MaRDI QIDQ2998684

Hirokazu Nishimura

Publication date: 18 May 2011

Abstract: In this paper, as the second in our series of papers on differential geometry of microlinear Frolicher spaces, we study differenital forms. The principal result is that the exterior differentiation is uniquely determined geometrically, just as grad (ient), div (ergence) and rot (ation) are uniquely determined geometrically or physically in classical vector calculus. This infinitesimal characterization of exterior differentiation has been completely missing in orthodox differential geometry.

Full work available at URL: https://arxiv.org/abs/1003.4317

zbMATH Keywords

synthetic differential geometryWeil algebraCartesian closed categoryWeil functorFrölicher spacenilpotent infinitesimalTopos theoryCahiers Toposinfinite-dimensional differential geeomerymicrolinearitytransversal limit diagram

Mathematics Subject Classification ID

Differential forms in global analysis (58A10) Synthetic differential geometry (51K10) Topos-theoretic approach to differentiable manifolds (58A03)

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Differential Geometry of Microlinear Frolicher Spaces I

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