Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Moreno

On Families in Differential Geometry

created by moreno on 15 Sep 2020



Inserted: 15 sep 2020
Last Updated: 15 sep 2020

Year: 2013

ArXiv: 1302.2061 PDF


Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows one to work without introducing ad hoc spaces, by using the language of differential calculus over commutative algebras. An advantage of such an approach, based on the notion of sliceable structures on cylinders, is that the fundamental theorems of standard calculus are straightforwardly generalized to the context of families. As an example of that, we prove the universal homotopy formula.

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