Università degli Studi di Genova


Singularities and regular paths (An elementary introduction to smooth homotopy)

This article is a basic introduction to a particular approach within smooth algebraic topology: our aim is to study 'smooth spaces with singularities', by methods of homotopy theory adapted to this task. Here we explore euclidean regions by paths of (variable) class C^k, counting their stops. The fundamental groupoid of the space acquires thus a sequence of integral C^k-weights that depend on a smoothness index; a sequence that can distinguish 'linear' singularities and their order. These methods can be applied to the theory of networks.

differential space, jet, singularity, homotopy groups

58, 55

Altre info:
MSC: 58A40, 58KXX, 58A20, 55Q05

Pubblicato su: Cahiers de Topologie et Geometrie Differentielle Categoriques Vol. 52 (2011) Pag. 45-76