Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 20th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexa brief entry on the result of * [[Ivan Limonchenko]], [[Zhi Lu]], [[Taras Panov]], _Calabi-Yau hypersurfaces and SU-bordism_, Proceedings of the Steklov Institute of Mathematics 302 (2018), 270-278 ([arXiv:1712.07350](https://arxiv.org/abs/1712.07350)) for ease of cross-linking in other entries (such as _[[MSU]]_, _[[K3]]_, _[[CY]]_) <a href="https://ncatlab.org/nlab/revision/Calabi-Yau+manifolds+in+SU-bordism+theory/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Calabi-Yau+manifolds+in+SU-bordism+theory">current</a>

   a brief entry on the result of

   • Ivan Limonchenko, Zhi Lu, Taras Panov, Calabi-Yau hypersurfaces and SU-bordism, Proceedings of the Steklov Institute of Mathematics 302 (2018), 270-278 (arXiv:1712.07350)

   for ease of cross-linking in other entries (such as MSU, K3, CY)

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 20th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexFixed the statement about the generation/span of SU-bordism classes by CYs. Now it reads as follows: *** The [[SU-bordism ring]] [[localization of a ring|away from 2]] is multiplicatively generated by [[Calabi-Yau manifolds]]. There are [[Calabi-Yau manifolds]] of complex dimension $3$ and $4$ whose whose SU-bordism classes equal the generators $\pm y_6$ and $\pm y_8$ in Prop. \ref{SUBordismRingAwayFromTwo}. Together with the [[K3 surface]] representing $- y_4$, this means that [[CYs]] [[linear space|span]] $\Omega^{SU}_{\leq 8}\big[ \tfrac{1}{2}\big]$. *** <a href="https://ncatlab.org/nlab/revision/diff/Calabi-Yau+manifolds+in+SU-bordism+theory/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/Calabi-Yau+manifolds+in+SU-bordism+theory/3">v3</a>, <a href="https://ncatlab.org/nlab/show/Calabi-Yau+manifolds+in+SU-bordism+theory">current</a>

   Fixed the statement about the generation/span of SU-bordism classes by CYs. Now it reads as follows:

   ---

   The SU-bordism ring away from 2 is multiplicatively generated by Calabi-Yau manifolds.

   There are Calabi-Yau manifolds of complex dimension $3$ and $4$ whose whose SU-bordism classes equal the generators $\pm y_6$ and $\pm y_8$ in Prop. \ref{SUBordismRingAwayFromTwo}.

   Together with the K3 surface representing $- y_4$, this means that CYs span $\Omega^{SU}_{\leq 8}\big[ \tfrac{1}{2}\big]$.

   ---

   diff, v3, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 20th 2020
   • (edited Nov 20th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexFurther adjustment. Should be correct now, but deserves to be expanded further.

   Further adjustment. Should be correct now, but deserves to be expanded further.