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nLab > Latest Changes: Analysis Situs

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 26th 2021

    a category:reference-entry

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 19th 2023
    • (edited Feb 19th 2023)

    When explaining the role of homotopy theory in physics, a recurring stumbling block is that the physicist says “topological” for phenomena that the mathematician would call homotopical (the mathematician in their right mind, that is, ignoring here misnomers like “THH” and its cousins…): such as in “topological field theory” or “topological quantum computation”.

    Vague reference question:

    Is there a good reference which would be illuminating to point the interested outsider to on this terminology issue and maybe highlighting the joint etymology of “topology” and “homotopy”.

    For instance, the article listed in the entry Analysis Situs starts out explaining topology to such an interested outsider, but at some point just starts using the word “homotopy” instead, without warning, explanation or comment.

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeFeb 20th 2023

    Re #2: We already have an article on this exact aspect: https://ncatlab.org/nlab/show/homotopy+theory+FAQ#intro. It has quite a few quotations from well-known sources.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 20th 2023

    Ah, thanks!! I had forgotten about the existence of that entry. These are useful quotes for what I am after, yes. Thanks.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTime3 hours ago

    added some texts also on Leibniz’s original proposal for an “analysis situs”:

    • Matthew McMillan: Geometric Quantity in Leibniz’s Analysis Situs, PhD thesis, Oxford (2017) [pdf]

    • Vincenzo De Risi: Analysis Situs, the Foundations of Mathematics and a Geometry of Space, The Oxford Handbook of Leibniz, Oxford University Press (2018) 247-258 [hal:03059623, doi:10.1093/oxfordhb/9780199744725.013.22]

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTime3 hours ago
    • (edited 3 hours ago)

    also added pointer to:

    • Dirk Siersma: Poincaré and Analysis Situs, the beginning of algebraic topology, Nieuw Archief voor Wiskunde serie 5 vol 13 no. 3 (2012) 196- 200 [handle:1874/272371, pdf]

    diff, v3, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTime3 hours ago

    and to:

    diff, v3, current

1 to 7 of 7

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