2018/01/17 by Shmuel, Metz
Computer Science · Physics and Astronomy · Mathematics · #Digital Image Processing Techniques #Advanced Mathematical Theories and Applications #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1801.05775
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.