• Corpus ID: 119327323

Homotopy structures of smooth CW complexes

@article{Haraguchi2018HomotopySO,
  title={Homotopy structures of smooth CW complexes},
  author={Tadayuki Haraguchi},
  journal={arXiv: Algebraic Topology},
  year={2018}
}
  • T. Haraguchi
  • Published 15 November 2018
  • Mathematics
  • arXiv: Algebraic Topology
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. 
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2 Citations

2 Citations

Citation Type

Citation Type

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References

SHOWING 1-10 OF 16 REFERENCES
Model categories of smooth spaces
We construct a model structure on the category of diffeological spaces whose weak equivalences are just smooth maps inducing isomorphisms on smooth homotopy groups. Our approach applies to the…
A model structure on the category of diffeological spaces
We construct a model category structure on the category of diffeological spaces which is Quillen equivalent to the model structure on the category of topological spaces based on the notions of Serre…
Homology and cohomology via enriched bifunctors
We show that the category of numerically generated pointed spaces is complete, cocomplete, and monoidally closed with respect to the smash product, and then utilize these features to establish a…
Quillen equivalences between the model categories of smooth spaces, simplicial sets, and arc-gengerated spaces
In the preceding paper, we have constructed a compactly generated model structure on the category $\dcal$ of diffeological spaces together with the adjoint pairs $|\ |_\dcal : \scal \rightleftarrows…
Mayer–Vietoris Sequence for Differentiable/Diffeological Spaces
The idea of a space with smooth structure is a generalization of an idea of a manifold. K. T. Chen introduced such a space as a differentiable space in his study of a loop space to employ the idea of…
Convenient Categories of Smooth Spaces
A "Chen space" is a set X equipped with a collection of "plots" - maps from convex sets to X - satisfying three simple axioms. While an individual Chen space can be much worse than a smooth manifold,…
Model category of diffeological spaces
  • Hiroshi Kihara
  • Mathematics
    Journal of Homotopy and Related Structures
  • 2018
The existence of a model structure on the category $${\mathcal {D}}$$D of diffeological spaces is crucial to developing smooth homotopy theory. We construct a compactly generated model structure on…
Diffeological vector pseudo-bundles
A Concise Course in Algebraic Topology
Differential Geometrical Methods in Mathematical Physics
...
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