Homotopy structures of smooth CW complexes

2018/11/15 by Tadayuki Haraguchi, Haraguchi, Tadayuki
Mathematics · #55P10 #55Q05 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 18G55 #Secondary 55P05

paper · pdf · doi:10.48550/arxiv.1811.06175

openalex publication_date 2018/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Quillen equivalences between the model categories of smooth spaces, simplicial sets, and arc-gengerated spaces
• On homotopy types of diffeological cell complexes

Related

• On homotopy types of diffeological cell complexes
• A geometric decomposition of spaces into cells of different types
• The Uniform Homotopy Category
• The Whitehead exact sequence and the classification problem of homotopy types
• Cubical setting for discrete homotopy theory, revisited