Deformations of normed groupoids and differential calculus. First part

Details Deformations of normed groupoids and differential calculus. First part Deformations of normed groupoids and differential calculus. First part

2009-11-06

arxiv.org/abs/0911.1300v1

Mathematics

Metric Geometry

Scientific paper

Differential calculus on metric spaces is contained in the algebraic study of normed groupoids with $\delta$-structures. Algebraic study of normed groups endowed with dilatation structures is contained in the differential calculus on metric spaces. Thus all algebraic properties of the small world of normed groups with dilatation structures have equivalent formulations (of comparable complexity) in the big world of metric spaces admitting a differential calculus. Moreover these results non trivially extend beyond metric spaces, by using the language of groupoids.

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