6 papers
Condensed Sets on Compact Hausdorff Spaces
Koji Yamazaki
A condensed set is a sheaf on the site of Stone spaces and continuous maps. We prove that condensed sets are equivalent to sheaves on the site of compact Hausdorff spaces and conti…
Fibration structure for Gromov h-principle
Koji Yamazaki
The h-principle is a powerful tool for obtaining solutions to partial differential inequalities and partial differential equations. Gromov discovered the h-principle for the genera…
Construction of an Engel manifold with trivial automorphism group
K. Yamazaki
An Engel manifold is a 4-manifold with a completely non-integrable 2-distribution called Engel structure. I research the functorial relation between Engel manifolds and Contact 3-o…
Sheaf theoretic characterization of etale groupoids
Koji Yamazaki
The study of Haeflier suggests that it is natural to regard a pseudogroup as an etale groupoid. We show that any etale groupoid corresponds to a pseudogroup sheaf, a new generaliza…
Developing Maps and Engel Automorphisms
Koji Yamazaki
A completely nonintegrable -dimensional distribution on a -manifold is called an Engel structure. A -manifold with an Engel structure is called an Engel manifold. The deve…
Engel Manifolds and Contact 3-Orbifolds
Koji Yamazaki
In early study of Engel manifolds from R. Montgomery, the Cartan prolongation and the development map are central figures. However, the development map can be globally defined only…