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 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 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

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 6th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a bit to _[[framed manifold]]_

   added a bit to framed manifold

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 6th 2013
   • (edited Nov 6th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexfixed a silliness at _[[framed manifold]]_, due to me, which somebody kindly pointed out by email (the alleged proof that every orientable 3-manifold admits a framing had really been the trivial argument that every spin 3-manifold admits a framing, instead of the non-tautological argument that $w_2$ also vanishes) fixed now.

   fixed a silliness at framed manifold, due to me, which somebody kindly pointed out by email (the alleged proof that every orientable 3-manifold admits a framing had really been the trivial argument that every spin 3-manifold admits a framing, instead of the non-tautological argument that $w_2$ also vanishes) fixed now.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexafter the example of the parallelizable sphereas I added the remark on division algebras and pointers to Adam's original proof.

   after the example of the parallelizable sphereas I added the remark on division algebras and pointers to Adam’s original proof.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeSep 3rd 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded brief remark ([here](http://ncatlab.org/nlab/show/framed+manifold#IntersectionPairing)) on relation to intersection pairing and Kervaire invariant.

   added brief remark (here) on relation to intersection pairing and Kervaire invariant.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeSep 11th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexdid a bunch of little edits today on the $n$Lab while the $n$Formum was out of business. Now I don't have the energy to announce them all. There were a few related to framings.

   did a bunch of little edits today on the $n$Lab while the $n$Formum was out of business. Now I don’t have the energy to announce them all. There were a few related to framings.

6. • CommentRowNumber6.
   • CommentAuthorDavidRoberts
   • CommentTimeJul 17th 2017
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI added to [[framed manifold]] some results about which left invariant framings on compact simple simply-connected Lie groups give nontrivial elements in stable homotopy groups of spheres. There is a conjecture that for semisimple compact connected Lie groups with rank bigger than some fixed constant, all of the associated stable homotopy elements are zero. The guess for the constant is at or below 10, and the known facts show that for _simple_ such Lie groups, at rank 4 and above this is true.

   I added to framed manifold some results about which left invariant framings on compact simple simply-connected Lie groups give nontrivial elements in stable homotopy groups of spheres.

   There is a conjecture that for semisimple compact connected Lie groups with rank bigger than some fixed constant, all of the associated stable homotopy elements are zero. The guess for the constant is at or below 10, and the known facts show that for simple such Lie groups, at rank 4 and above this is true.

7. • CommentRowNumber7.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 28th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded a reference to an extension of left invariant framing to [[compact p-groups]] * [[Tilman Bauer]], _p-compact groups as framed manifolds_, ([paper](https://people.kth.se/~tilmanb/publication/p-compact-groups-as-framed-manifolds/)) <a href="https://ncatlab.org/nlab/revision/diff/framed+manifold/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/framed+manifold/20">v20</a>, <a href="https://ncatlab.org/nlab/show/framed+manifold">current</a>

   Added a reference to an extension of left invariant framing to compact p-groups

   • Tilman Bauer, p-compact groups as framed manifolds, (paper)

   diff, v20, current