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

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.

118 pages,16 figures generated by xy Processed by pdfTeX, Version 3.14159265-2.6-1.40.18 (MiKTeX 2.9.6350), LaTeX2e <2017-04-15> To be submitted to Mathematical Sciences Publishers for Geometry & Topology or Algebraic & Geometric Topology Private macros are used to simplify globally changing some typographic conventions to suit house styles