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 comma 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 finite 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 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).
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeOct 3rd 2011

    Hi everyone! I’m back from a 2-week vacation without Internet access. It’ll take me a little while to catch up on everything, but just so you know, I’m here again now….

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 3rd 2011
    • (edited Oct 3rd 2011)

    Good to hear that you are back!

    I was in Pittsburgh last week and spoke with some of the HoTT people there. Only through this conversation has it become clear to me that the HoTT derivation of

    π 1(S 1)= \pi_1 (S^1) = \mathbb{Z}

    that you had posted to the blog a while back is regarded as a big achievement in the field! I hear that Joyal is currently following a project for next computing π 3(S 2)\pi_3(S^2). Sounds like this is something that will keep HoTTists busy for a while. :-)

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 3rd 2011

    Welcome back! I figured that you were just hunkering down to research and avoiding getting distracted by internet stuff, forgetting that I too take internet-free vacations on occasion. :-)

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeOct 3rd 2011

    the HoTT derivation of π 1(S 1)=\pi_1 (S^1) = \mathbb{Z} that you had posted to the blog a while back is regarded as a big achievement in the field!

    That’s nice to hear; I haven’t actually talked to any of them in person since the HoTT Oberwolfach meeting. (-: I wonder what approach Joyal is taking to π 3(S 2)\pi_3(S^2). The “obvious” approach to me is to construct the Hopf fibration and prove the homotopy long exact sequence of a fibration, but it’s not obvious to me how to identify the total space of the Hopf fibration as being S 3S^3 (or, at least, 2-simply-connected). I guess that that approach would also first involve proving π n(S n)=\pi_n(S^n)=\mathbb{Z} at least for small nn, which one could maybe do with the Freudenthal suspension theorem.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 3rd 2011
    • (edited Oct 3rd 2011)

    Yes, apparently Joyal is going via the Hopf fibration. But that’s already all I have heard about it. (Apart from giving a talk to the whole group, I mostly chatted with Krzysztof Kapulkin, who told me these things.)