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: Pontryagin-Thom construction -- references

Bottom of Page

1 to 12 of 12

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 23rd 2020
    • (edited Dec 23rd 2020)

    this is a bare list of references, to be !include-ed into relevant entries

    (various parts of this list have been contained at Cohomotopy, Cohomotopy charge map, Thom’s theorem, Pontryagin-Thom construction and elsewhere; this here now to ease harmonizing/completing these lists)

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2021
    • (edited Feb 4th 2021)

    added pointer to:

    diff, v10, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2021

    added pointer to:

    diff, v11, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 5th 2021

    added pointer to:

    diff, v13, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeFeb 26th 2021

    added this pointer:

    The Pontrjagin theorem must have been known to Pontrjagin at least by 1936, when he announced the computation of the second stem of homotopy groups of spheres:

    • Lev Pontrjagin, Sur les transformations des sphères en sphères (pdf) in: Comptes Rendus du Congrès International des Mathématiques – Oslo 1936 (pdf)

    diff, v14, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 27th 2021

    I have added pointer to Theorem C in

    which seems to be the first place where the “Pontryagin-Thom theorem”, stably and for general tangential structure, is actually stated.

    diff, v15, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMar 3rd 2021

    added section (here) with references on generalization of the Pontrjagin theorem to a twisted/equivariant Pontrjagin theorem.

    (Currently the only items are Cruikshank’s, but maybe to be expanded)

    diff, v16, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMar 3rd 2021

    added a sub-section “Pontrjagin’s construction – In negative codimension” (here) with pointers to the “May-Segal theorem” (identifying Cohomotopy cocycle spaces with configuration spaces of points)

    (I should really give May-Segal theorem it’s own entry, since it’s somewhat buried at configuration space of points. But not right now.)

    diff, v16, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMar 3rd 2021
    • (edited Mar 3rd 2021)

    for what it’s worth, on the twisted Pontrjagin theorem (here) I have changed the wording from “straightforward generalization” to “fairly straightforward generalization” and added pointer to Cruickshanks’ Lemma-like Section 5.1, which, after all, takes him a full page.

    diff, v17, current

  10. fix title of Milnor book

    Anonymous

    diff, v19, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 8th 2023

    added pointer to:

    diff, v20, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJul 24th 2024
    • (edited Jul 24th 2024)

    added pointer to:

    diff, v22, current

1 to 12 of 12

  1.