Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: Analysis Situs

Bottom of Page

1 to 7 of 7

  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
    • CommentTime2 days 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
    • CommentTime2 days ago
    • (edited 2 days 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
    • CommentTime2 days ago

    and to:

    diff, v3, current

1 to 7 of 7

  1.