Defines categories of atlases for manifolds and fiber bundles together with functors among those categories to give a unified treatment.
Local Coordinate Spaces: a proposed unification of manifolds and fiber bundles, and associated machinery
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abstract
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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math.AT 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Towards a taxonomy of atlases and of morphisms between them
Defines categories of atlases for manifolds and fiber bundles together with functors among those categories to give a unified treatment.