Homotopy structures of smooth CW complexes

TL;DR

This paper introduces smooth CW complexes within diffeological spaces, exploring their homotopy structures and properties related to homotopy extension, advancing the understanding of smooth topological constructions.

Contribution

It defines smooth CW complexes using cubes in diffeological spaces and investigates their homotopy extension properties, a novel approach in smooth topology.

Findings

Established the notion of smooth CW complexes in diffeological spaces.

Analyzed the homotopy extension property for these complexes.

Provided foundational results for smooth homotopy theory.

Abstract

In this paper we present the notion of smooth CW complexes given by attaching cubes on the category of diffeological spaces, and we study their smooth homotopy structures related to the homotopy extension property.