Changes between Initial Version and Version 1 of Ticket #18175, comment 20


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Timestamp:
05/31/15 06:14:57 (5 years ago)
Author:
tscrim
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  • Ticket #18175, comment 20

    initial v1  
    11It still seems like we are having an assumption that all manifolds can inherently be realized over '''R'''. This was my initial assumption too, and so manifolds that could be locally homoemorphic to '''C'''^d^ were a special case.
    22
    3 However I feel like it would be best for `Manifolds` to be over an arbitrary topological field (which will require some very mild changes). So then the heirarchy for manifolds then be:
     3However I feel like it would be best for `Manifolds` to be over an arbitrary topological field (which will require some very mild changes). So then the heirarchy for manifolds would be:
    44{{{
    55     Manifolds
     
    1313             Complex
    1414}}}
    15 Do we think we should add a stub category for PL and/or (pseudo) Riemannian manifolds? How about `ManifoldsWithBoundary` as a supercategory of `Manifolds` (and how many of these extra structures lift to the boundary)?
     15Do you think this what we want?
     16
     17Also do we think we should add a stub category for PL and/or (pseudo) Riemannian manifolds? How about `ManifoldsWithBoundary` as a supercategory of `Manifolds` (and how many of these extra structures lift to the boundary)?
    1618
    1719A question for CW complexes, should the elements of a CW complex be the cells or the points of the topological space? Right now, I'm taking the former approach, but I feel this might be an abuse as these should be subobjects of the category (Nicolas, any wisdom to impart on this?). If this seems like a non-trivial issue, I can split this ticket into 2 parts; one for the manifolds and one for the CW complexes.