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 definitions 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 k-theory lie-theory limits linear linear-algebra locale localization logic mathematics 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 object 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: manifold diagram

Bottom of Page

1 to 9 of 9

  1.  
    • CommentRowNumber1.
    • CommentAuthorChristoph Dorn
    • CommentTimeSep 23rd 2022

    extended stub, including: - many motivational examples - a definitional sketch

    v1, current

    • CommentRowNumber2.
    • CommentAuthorChristoph Dorn
    • CommentTimeFeb 23rd 2023

    made definition explicit and self-contained, expanded article

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorChristoph Dorn
    • CommentTimeMar 13th 2023

    Added pointer to introductory n-category café post

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorChristoph Dorn
    • CommentTimeMar 14th 2023

    corrected terminology

    diff, v5, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2023

    Given that the terminology “framed” here clashes with its ordinary use, and given that ℝ n\mathbb{R}^n equipped with such “framing” is then called a “directed space” anyways (here), why not speak of a “direction” or the like, instead of a “framing”?

    • CommentRowNumber6.
    • CommentAuthorChristoph Dorn
    • CommentTimeMay 12th 2023

    I started writing “framed-directed” instead of “framed” in a few places where the context isn’t clear, and I hope that improves the situation a bit. “Framed-directed” can then be abbreviated to “framed” if the context is clear. The following points were considered when the terminology was chosen:

    • “directed” is a highly used term. in particular, the term “directed topological space” refers to a general idea and less so to a concrete notion. there are various ways of making that term concrete though, “framed-directed” topological spaces are one of them.
    • the notion of “framed-directedness” and “ordinary framedness” are closely related (as explained to some extent at directed topological space). for instance, every stratum in a manifold diagrams is a framed manifold (in the ordinary sense). Moreover, a “framed-directed space” XX, if XX is a manifold, is in particular a “ordinarily framed (namely, parallelizable) manifold XX”. Generally, I’d argue that “framings” always refer to “choosing directions” in one way or the other.
    • While “framed manifold” has an agreed-upon meaning, “framed (stratified) space” doesn’t yet.
    • The terminology has been used with similar meaning in the context of stratified spaces in the work of Ayala-Francis-Tanaka-Rozenblyum: namely, they speak of “vari-framings”.
    • CommentRowNumber7.
    • CommentAuthorChristoph Dorn
    • CommentTimeMay 12th 2023

    highlighting combinatorialization property

    diff, v8, current

    • CommentRowNumber8.
    • CommentAuthorChristoph Dorn
    • CommentTimeJun 3rd 2023
    • added talk reference

    diff, v9, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeNov 16th 2023
    • (edited Nov 18th 2023)

    added pointer to:

    diff, v10, current

1 to 9 of 9

  1.