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 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 nforum 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 sheaves 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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2020

    Just for completeness, to go with e-invariant and f-invariant.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 2nd 2020

    We don’t yet have a page for f-invariant.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2020

    spelled out (here) the example of how the d-invariant specializes to the ordinary Hopf degree.

    Am adding this example now also to degree of a continuous function and to Hopf degree theorem

    diff, v5, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 15th 2021
    • (edited Jan 15th 2021)

    I have added a section “Trivializations of the d-invariant” (here) with some observations.

    While from a modern abstract homotopy-theoretic perspective this is really a one-line observation, unwinding this accounts for (and completes) a fair bit of argument in Section 16 of Conner-Floyd’s 66 book (for which no modernized account seems to exist?!), and it also sets the pattern for the other classical constructions of the e-invariant and the Hopf invariant.

    So therefore I thought it would be useful to spell this out a little. Also, this section provides details now linked to at MUFr and at Adams e-invariant – Construction via unit cofiber cohomology theories.

    diff, v6, current

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 15th 2021

    Some new candidates for a HoTT treatment?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 15th 2021

    I had had that same thought, yes. The style of construction that I am writing out at Adams e-invariant – Construction via cofiber theories should lends itself to full formalization in HoTT. For instance the Conner-Floyd theorem becomes a formal corollary by factoring a homotopy pasting diagram (here) .

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJan 15th 2021

    have added the diagrams for the “quick abstract proof” (here)

    diff, v7, current