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 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

1. • CommentRowNumber1.
   • CommentAuthorRichard Williamson
   • CommentTimeSep 25th 2016
   • (edited Sep 25th 2016)
   • PermaLink
   Author: Richard Williamson
   Format: MarkdownItexHello all, I would like to discuss a revitalisation of the approach to the Poincaré conjecture that I have discussed a couple of times this year. I have always felt that this approach has something going for it, and some new ideas that I had recently hopefully allow me to complete the loose ends from before, and explain the argument in a way that it can be understood. See [this document](http://rwilliamson-mathematics.info/miscellaneous/nforum--knot_case.pdf) for the argument in the case of knots. I would like to emphasise that all of the geometrical manipulations in this argument are very concrete, and can be explored in examples with pen and paper. If anyone needs any help with this, let me know. They could be even be carried out on a computer, virtual knots being eminently suitable for this. Several readers of the nForum have kindly shown an interest in these ideas in the past: Noam, Todd, and David Roberts, I especially remember. If any of you are interested in taking a look at the latest incarnation of these ideas, I'd be grateful. I'm thinking of trying to persuade some experts to drop by here and take a look, and am hoping to write a guest post on the n-café with a slightly more gentle exposition, giving more background, if things seem to be holding up.

   Hello all,

   I would like to discuss a revitalisation of the approach to the Poincaré conjecture that I have discussed a couple of times this year. I have always felt that this approach has something going for it, and some new ideas that I had recently hopefully allow me to complete the loose ends from before, and explain the argument in a way that it can be understood.

   See this document for the argument in the case of knots.

   I would like to emphasise that all of the geometrical manipulations in this argument are very concrete, and can be explored in examples with pen and paper. If anyone needs any help with this, let me know. They could be even be carried out on a computer, virtual knots being eminently suitable for this.

   Several readers of the nForum have kindly shown an interest in these ideas in the past: Noam, Todd, and David Roberts, I especially remember. If any of you are interested in taking a look at the latest incarnation of these ideas, I’d be grateful. I’m thinking of trying to persuade some experts to drop by here and take a look, and am hoping to write a guest post on the n-café with a slightly more gentle exposition, giving more background, if things seem to be holding up.

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeSep 28th 2016
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexRegarding the prior discussion, I seem to recall that Emily Riehl zeroed in on points of your argument that were delicate. Is she aware of these more recent developments? She might be an ideal interlocutor (among people who now and then drop by here).

   Regarding the prior discussion, I seem to recall that Emily Riehl zeroed in on points of your argument that were delicate. Is she aware of these more recent developments? She might be an ideal interlocutor (among people who now and then drop by here).

3. • CommentRowNumber3.
   • CommentAuthorRichard Williamson
   • CommentTimeSep 28th 2016
   • PermaLink
   Author: Richard Williamson
   Format: MarkdownItexThanks Todd, yes, Emily is aware of my post here, and has kindly offered to put a guest post which I plan to write about this on the n-café. She is very busy at the moment, but I would of course indeed be delighted if she is able to drop by. :-)

   Thanks Todd, yes, Emily is aware of my post here, and has kindly offered to put a guest post which I plan to write about this on the n-café. She is very busy at the moment, but I would of course indeed be delighted if she is able to drop by. :-)

4. • CommentRowNumber4.
   • CommentAuthorDavidRoberts
   • CommentTimeSep 28th 2016
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexLet me just say that I'm still interested to see where this goes, but I haven't particularly invested the time to understand what you've written in any deep way.

   Let me just say that I’m still interested to see where this goes, but I haven’t particularly invested the time to understand what you’ve written in any deep way.

5. • CommentRowNumber5.
   • CommentAuthorRichard Williamson
   • CommentTimeDec 23rd 2016
   • PermaLink
   Author: Richard Williamson
   Format: MarkdownItexI've now made a more visibly public of these ideas (in their latest incarnation, a slight tweaking of those in #1; the new idea being use of virtual knot theory) at the [n-café](https://golem.ph.utexas.edu/category/2016/12/globular_for_higherdimensional.html#c051685).

   I’ve now made a more visibly public of these ideas (in their latest incarnation, a slight tweaking of those in #1; the new idea being use of virtual knot theory) at the n-café.