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: MSU

Bottom of Page

1 to 10 of 10

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2020

    starting something

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020
    • (edited Nov 20th 2020)

    added this pointer:

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    added pointer to:

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020
    • (edited Nov 20th 2020)

    added the statement that

    the SU-bordism ring is spanned by classes of Calabi-Yau manifolds: in particular the K3 surface in degree 4 and certain CY 3-folds and CY4-folds in degrees 6 and 8.

    Will give this statement its own little entry now (Calabi-Yau manifolds in SU-bordism theory), for ease of cross-linking in the entries K3 surface and Calabi-Yau manifold

    diff, v2, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    added pointer to:

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    added these statements:

    The kernel of the forgetful morphism

    Ω • SU⟶Ω • U \Omega^{SU}_\bullet \longrightarrow \Omega^{\mathrm{U}}_\bullet

    from the SU-bordism ring to the complex bordism ring, is pure torsion.

    Every torsion element in the SU-bordism ring Ω • SU\Omega^{SU}_\bullet has order 2.

    diff, v3, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    and this one:

    The torsion subgroup of the SU-bordism ring is concentrated in degrees 8k+18k+1 and 8k+28k+2, for k∈ℕk \in \mathbb{N}.

    diff, v3, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 9th 2021

    added pointer to:

    diff, v7, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2021
    • (edited Feb 18th 2021)

    I have made explicit the corollary (here) that the image of the element [K3][K3] of Ω 4 SU\Omega^{SU}_4 is still non-trivial in Ω 4 U\Omega^{\mathrm{U}}_4.

    (This must be well-known, but I have trouble finding a reference that says it more directly. A half-sentence in Novikov 86, p. 216 (218 of 321) suggests this, without, however, really saying so, much less proving it.)

    diff, v10, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2021

    added pointer to:

    for (the failure of) the Conner-Floyd isomorphism for MSU→KOMSU \to KO.

    diff, v11, current

1 to 10 of 10

  1.