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Jones’s new polynomial | Low Dimensional Topology
https://ldtopology.wordpress.com/2015/01/14/joness-new-polynomial
January 14, 2015. Jones’s new polynomial. Filed under: Knot theory. 8212; dmoskovich @ 11:05 am. Check out this exciting new preprint by Vaughan Jones! VFR Jones, Some Unitary Representations of Thompson’s Groups. Links occur as braid closures, and so links can be studied via braid theory. This is the starting point for the Jones polynomial. And it’s very nice, because braids form a group (good algebraic property) which is orderable (even biorderable) and automatic. Je ne sais quoi. And elements of Thomp...
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The academic spring fails… or does it? | Low Dimensional Topology
https://ldtopology.wordpress.com/2015/06/19/the-academic-spring-fails-or-does-it
June 19, 2015. The academic spring fails… or does it? Filed under: Academic publishing. 8212; dmoskovich @ 5:40 am. A few hours ago, Math2.0, the discussion forum for journal publishing reform, closed for good. This is an indicator that the Cost of Knowledge. On the converse side, there are a lot of new OA journals out there, some Green and some Gold. This is a very good thing! Submit there, and we can beat predatory publishers through market competition. 3 Comments ». Comment by Greg Friedman. In any ev...
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MOO is classical | Low Dimensional Topology
https://ldtopology.wordpress.com/2015/03/30/moo-is-classical
March 30, 2015. 8212; dmoskovich @ 9:43 am. The simplest quantum 3-manifold invariant is the Murakami-Ohtsuki-Okada (MOO) invariant. It comes from. Chern-Simons theory in the way that the. Reshetikhin-Turaev invariant comes from. Chern-Simons Theory. It has a closed formula in terms of the order of the first cohomology class of the. And an eighth root of unity. Witten’s Chern-Simons theory for gauge group. A recently published paper by Gelca and Uribe. Which is also the topic of a book by Gelca. I’...
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Tangle diagram crossings and quantum entanglement | Low Dimensional Topology
https://ldtopology.wordpress.com/2015/07/28/tangle-diagram-crossings-and-quantum-entanglement
July 28, 2015. Tangle diagram crossings and quantum entanglement. 8212; dmoskovich @ 1:55 pm. In low dimensional topology we speak of tangles, while quantum physics speaks of entanglement. Similar words, but is there a deeper connection? Kauffman conjectured that the answer is yes. And I think he’s right, although maybe for other reasons). Glancing through arXiv this morning, I came across the following recent preprint:. Alagic, G., Jarret M., and Jordan S.P. But are inseparably intertwined in that they ...
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Complex hyperbolic geometry of knot complements | Low Dimensional Topology
https://ldtopology.wordpress.com/2015/03/09/complex-hyperbolic-geometry-of-knot-complements
March 9, 2015. Complex hyperbolic geometry of knot complements. 8212; dmoskovich @ 3:41 am. This morning there was a paper which caught my eye:. Deraux, M. and Falbel, E. 2015 Complex hyperbolic geometry of the figure-eight knot. In it, the authors study a very different geometric structure for the figure-eight knot complement, as the manifold at infinity of a complex hyperbolic orbifold. The largest subbundle in the tangent bundle that is invariant under the complex structure) of. CR structures are very...
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Associativity vs. Distributivity | Low Dimensional Topology
https://ldtopology.wordpress.com/2014/07/21/associativity-vs-distributivity
July 21, 2014. Associativity vs. Distributivity. Filed under: Racks and quandles. 8212; dmoskovich @ 7:04 am. Examples of associative operations include addition, multiplication, connect-sum, disjoint union, and composition of maps. Then the operation is said to be self-distributive. Examples of self-distributive operations include conjugation. Assume X and Y are both Gaussian so that such a binary operation makes sense, essentially as covariance intersection. Elements of a real vector space. The associa...
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SnapPy 2.3 released | Low Dimensional Topology
https://ldtopology.wordpress.com/2015/03/22/snappy-2-3-released
March 22, 2015. SnapPy 2.3 released. 8212; Nathan Dunfield @ 2:25 pm. Marc Culler and I are pleased to announce version 2.3 of SnapPy. Major improvements to the link and planar diagram component. Including link simplification, random links, and better documentation. Basic support for spun normal surfaces. New extra features when used inside of Sage:. HIKMOT-style rigorous verification of hyperbolic structures. Contributed by Matthias Goerner. Many basic knot/link invariants. Lipschitz and Jennet Dickinson.
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Slice-ribbon progress | Low Dimensional Topology
https://ldtopology.wordpress.com/2015/06/11/slice-ribbon-progress
June 11, 2015. 8212; dmoskovich @ 10:29 am. There has been some recent interesting progress around the Slice Ribbon Conjecture. In particular, Yasui is giving talks on an infinite family counterexamples to the Akbulut-Kirby Conjecture (1978) that he has constructed:. If 0-surgeries on two knots give the same 3-manifold, then the knots with relevant orientations are concordant. Leave a Comment ». Feed for comments on this post. Leave a Reply Cancel reply. Enter your comment here. Address never made public).
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Recent coloured HOMFLYPT-related stuff | Low Dimensional Topology
https://ldtopology.wordpress.com/2015/05/22/recent-progress-in-coloured-homflypt-stuff
May 22, 2015. Recent coloured HOMFLYPT-related stuff. Filed under: Knot theory. 8212; dmoskovich @ 10:41 am. One of the main ways in which I keep my finger on the pulse of what is hot now in low dimensional topology is to write lots and lots of reviews, both for Zentralblatt MATH. And also for MathSciNet. In the last year or so, what has been increasingly coming through the pipe is papers about knot homology. There seems to be a lot happening in this field right now. 8211;dimensional Chern-Simons theory.
