arXiv subjects
Publications and source records attributed to Tadayuki Haraguchi.
In this paper, we present the Baumkuchen Theorem related to the combination of divided Baumkuchen pieces. It can be proved using the basic properties of elementary geometry. We also apply some lemmas to prove the Pizza Theorem.
We construct on the category of diffeological spaces a Quillen model structure having smooth weak homotopy equivalences as the class of weak equivalences.
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.
We introduce the notion of smooth cell complexes and its subclass consisting of gathered cell complexes within the category of diffeological spaces (cf. Definitions 1 and 3). It is shown that the following hold. (1) With respect to the D-topology, every smooth cell complex is a topological cell complex (cf. Proposition 2). It is paracompact and Hausdorff if it is countable (cf. Proposition 8). (2) Every continuous map between gathered cell complexes is continuously homotopic to a smooth map (cf. Theorem 5). (3) Any topological cell complex is continuously homotopy equivalent to a gathered (hence smooth) cell complex (cf. Theorem 6). (4) Every D-open cover of a smooth countable cell complex has a subordinate partition of unity by smooth functions (cf. Theorem 9).
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 fibrations and weak homotopy equivalences.
In this paper we present the notion of de Rham cohomology with compact support for diffeological spaces. Moreover we shall discuss the existence of three long exact sequences. As a concrete example, we show that long exact sequences exist for the de Rham cohomology of diffeological subcartesian spaces.
Let $\bf C$ be a coreflective subcategory of a cofibrantly generated model category $\bf D$. In this paper we show that under suitable conditions $\bf C$ admits a cofibrantly generated model structure which is left Quillen adjunct to the model structure on $\bf D$. As an application, we prove that well-known convenient categories of topological spaces, such as $k$-spaces, compactly generated spaces, and $Δ$-generated spaces \cite{DN} (called numerically generated in \cite{KKH}) admit a finitely generated model structure which is Quillen equivalent to the standard model structure on the category $\bf Top$ of topological spaces.