Local Coordinate Spaces: a proposed unification of manifolds and fiber bundles, and associated machinery

Shmuel (Seymour J.) Metz

arxiv: 1801.05775 · v1 · pith:RTBLNHACnew · submitted 2018-01-17 · 🧮 math.AT

Local Coordinate Spaces: a proposed unification of manifolds and fiber bundles, and associated machinery

Shmuel (Seymour J.) Metz This is my paper

classification 🧮 math.AT

keywords bundlesfibermanifoldscoordinatedefineslocalalongassociated

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This paper presents a unified view of manifolds and fiber bundles, which, while superficially different, have strong parallels. It introduces the notions of an m-atlas and of a local coordinate space, and shows that special cases are equivalent to fiber bundles and manifolds. Along the way it defines some convenient notation, defines categories of atlases, and constructs potentially useful functors.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Towards a taxonomy of atlases and of morphisms between them
math.AT 2019-06 unverdicted novelty 4.0

Defines categories of atlases for manifolds and fiber bundles together with functors among those categories to give a unified treatment.