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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Legendrian knots and cluster algebras via augmentations
Legendarian结 簇代数 增广
2023/5/16
Legendrian knots and their exact Lagrangian fillings are central objects to study in low dimensional contact and symplectic topology. In recent developments, cluster algebras have proven to be powerfu...
Got rope? Then try this experiment: Cross both ends, left over right, then bring the left end under and out, as if tying a pair of shoelaces. If you repeat this sequence, you get what’s called a “gran...
Adaptive Priors based on Splines with Random Knots
Adaptive estimation bayesian non-parametric optimal contrac-tion rate spline random knots
2013/4/27
Splines are useful building blocks when constructing priors on nonparametric models indexed by functions. Recently it has been established in the literature that hierarchical priors based on splines w...
The “Kiel Knots” Technique for Treatment of Congenital and Acquired Penile Deviation
Congenital Penile Deviation Acquired Penile Deviation Peyronie’s Disease Penile Shortening
2013/1/29
Objectives: We propose a surgical correction of the penile curvature applying a technique based on the 16-dot plication technique modified by burying the knots in a shallow trough of incised tunica. W...
Seifert fibered surgery on Montesinos knots
Exceptional Dehn surgery hyperbolic knots Montesinos knots
2012/7/11
Exceptional Dehn surgeries on arborescent knots have been classified except for Seifert fibered surgeries on Montesinos knots of length 3. There are infinitely many of them as it is known that 4n+6 an...
Twisted Alexander polynomials of 2-bridge knots
Twisted Alexander polynomials 2-bridge knots Geometric Topology
2012/6/30
We investigate the twisted Alexander polynomial of a 2-bridge knot associated to a Fox coloring. For several families of 2-bridge knots, including but not limited to, torus knots and genus-one knots, ...
Unknotting numbers and triple point cancelling numbers of torus-covering knots
Surface knot 2-dimensional braid quandle cocycle invariant unknotting number triple point cancelling number
2012/6/21
It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additions. The minimum numb...
This thesis develops some general calculational techniques for finding the orders of knots in the topological concordance group C. The techniques currently available in the literature are either too t...
Arc index of pretzel knots of type $(-p,q,r)$
knot pretzel knot arc presentation arc index Kauffman polynomial
2012/4/18
We computed the arc index for the pretzel knots $K=P(-p,q,r)$ with $p,q,r\ge2$, $r\geq q$ and at most one of $p,q,r$ is even. If $q=2$, then the arc index $\alpha(K)$ equals the minimal crossing numbe...
This report presents a unified treatment of the density of states for the knots and folds of polymer chains. The physical realization of such systems ranges from DNA molecules to the microscopic confi...
Monopole Floer homology and Legendrian knots
Monopole Floer homology Legendrian knots Symplectic Geometry
2011/9/29
Abstract: We use monopole Floer homology for sutured manifolds to construct invariants of Legendrian knots in a contact 3-manifold. These invariants assign to a knot K in Y elements of the monopole kn...
Alexander Polynomial Invariants of Torus Knots T(n,3) and Chebyshev Polynomials
Alexander Polynomial Invariants Chebyshev Polynomials Mathematical Physics
2011/9/22
Abstract: The explicit formula, which expresses the Alexander polynomials \Delta_{n,3}(t) of torus knots T(n,3) as a sum of the Alexander polynomials \Delta_{k,2}(t) of torus knots T(k,2), is found. U...
On Virtual Crossing Numbers for Virtual Knots
Knot virtual knot graph crossing number parity
2011/9/20
Abstract: The aim of the present paper is to prove that the minimal number of virtual crossings for some families of virtual knots grows quadratically with respect to the minimal number of classical c...
Detection of Chirality and Mutations of Knots and Links
chirality mutation Chern-Simons field theory invariants
2011/9/30
Abstract: In this brief presentation, we would like to present our attempts of detecting chirality and mutations from Chern-Simons gauge theory. The results show that the generalised knot invariants, ...
Cosmetic crossings of genus one knots
cosmetic crossing nugatory crossing Thurston norm pretzel knot Whitehead double
2011/9/1
Abstract: We show that for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application we prove ...