A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New proof for minimizing tunnel systems in satellite chain links.
Fix an integer N>1. To each diagram of a link colored by 1,...,N, we associate a chain complex of graded matrix factorizations. We prove that the homotopy type of this chain complex is invariant under Reidemeister moves. When every component of the link is colored by 1, this chain complex is isomorphic to the chain com…
Determines surgeries on chain links bounding rational homology balls using lattice-theoretic methods.
We classify all the exceptional Dehn surgeries on the minimally twisted chain links with six and seven components.
We prove the volume conjecture for an infinite family of links called Whitehead chains that generalizes both the Whitehead link and the Borromean rings.
New shifting chain map enhances quandle invariants for links.
Researchers determine the Thurston unit ball for a family of -chained links and find conditions for fibered faces.
Maps quandle homology to relative group homology.
Link Floer homology is split into snake complexes and local systems.
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formal…
Study reveals supply chain correlations in firm growth rates.
We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking …
Using Kirby Calculus, we explicitly pass from Berge's R-R descriptions of ten families of knots with lens space surgeries to surgery descriptions on the minimally twisted five chain link (MT5C). Since the MT5C admits a strong involution, we also give the corresponding tangle descriptions.
The paper develops new inequalities for Markov chain sums, linking them to mixing time.
Computes homology of an obstruction chain complex in grid homology.
Extends Jones' construction to Thompson's group F and link homology.
For knots in S^3, the bi-graded hat version of knot Floer homology is defined over Z; however, for a link L in S^3 with #|L|=l>1, there are 2^{l-1} bi-graded hat versions of link Floer homology defined over Z, the multi-graded hat version of link Floer homology is only defined over F_2 from holomorphic considerations, …
In Part I of this paper we introduced the notion of the projective linking number Link(M,Z) of a compact oriented real submanifold M of dimension 2p-1 in complex projective n-space P^n with an algebraic subvariety Z of codimension p in P^n - M. It is shown here that a basic conjecture concerning the projective hull of …
Geometrically interprets a duality theorem linking cochain and chain complexes.
We construct cobordism maps on link Floer homology associated to decorated link cobordisms. The maps are defined on a curved chain homotopy type invariant. We describe the construction, and prove invariance. We also make a comparison with the graph TQFT for Heegaard Floer homology.
Khovanov homology for links in S^3 via 1-tangle diagrams in annulus.
The paper presents a chain complex for 3-manifold covers, including surface bundles and surgeries.
New proof found for Khovanov's assertion about Frobenius algebra twists.
Let L be a link in an integral homology three-sphere. We give a description of the Heegaard Floer homology of integral surgeries on L in terms of some data associated to L, which we call a complete system of hyperboxes for L. Roughly, a complete systems of hyperboxes consists of chain complexes for (some versions of) t…
It has been observed that most manifolds in the Callahan-Hildebrand-Weeks census of cusped hyperbolic -manifolds are obtained by surgery on the minimally twisted 5-chain link. A full classification of the exceptional surgeries on the 5-chain link has recently been completed. In this article, we provide a complete cl…
We give chain homotopy maps of Khovanov-type link homology of a universal differential. The universal differential, discussed by Mikhail Khovanov, Marco Mackaay, Paul Turner and Pedro Vaz, contains the original Khovanov's differential and Lee's differential. We also consider the conditions of any differential ensuring …
Study the JSJ-decomposition of a specific 3-manifold.
Study reveals hidden accidental parabolics in complex hyperbolic geometry.
New hyperbolic links have more symmetries than their complements.
Our work sheds new light on the role of oil prices in shaping the world economy by investigating flows of goods and services through global value chains between 1960 and 2011, by means of Markov Chain and network analysis. We show that over that time period the international division of labor and trade patterns are tig…
We introduce a generalization of the Lisca-Ozsváth-Stipsicz-Szabó Legendrian invariant to links in every rational homology sphere, using the collapsed version of link Floer homology. We represent a Legendrian link in a contact 3-manifold with a diagram , given by an open book decomposition …
Agol has conjectured that minimally twisted n-chain links are the smallest volume hyperbolic manifolds with n cusps, for n at most 10. In his thesis, Venzke mentions that these cannot be smallest volume for n at least 11, but does not provide a proof. In this paper, we give a proof of Venzke's statement for a number of…
Supply chains are the backbone of the global economy. Disruptions to them can be costly. Centrally managed supply chains invest in ensuring their resilience. Decentralized supply chains, however, must rely upon the self-interest of their individual components to maintain the resilience of the entire chain. We examine t…
In this paper, we focus on L-spaces for which the boundary maps of the Heegaard Floer chain complexes vanish. We collect such manifolds systematically by using the smoothing order on links.
Preserves hyperbolicity in link complements with two moves.
We compute different versions of link Floer homology and for any -space link with two components. The main approach is to compute the -function of the filtered chain complex which is determined by the Alexander polynomials of every sublink of the -space link. As an application, Thurst…
For a Morse function f on a compact oriented manifold M, we show that f has more critical points than the number required by the Morse inequalities if and only if there exists a certain class of link in M whose components have nontrivial linking number, such that the minimal value of f on one of the components is large…
In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion of torsion generalizes the torsion of acyclic based chain complexes, and is a ch…
We have conducted an agent-based simulation of chain bankruptcy. The propagation of credit risk on a network, i.e., chain bankruptcy, is the key to nderstanding largesized bankruptcies. In our model, decrease of revenue by the loss of accounts payable is modeled by an interaction term, and bankruptcy is defined as a ca…
Researchers find optimal configurations of complex knots and links.
Study analyzes fees linked to VIX index in annuity contracts.
We define several homology theories for central hyperplane arrangements, categorifying well-known polynomial invariants including the characteristic polynomial, Poincare polynomial, and Tutte polynomial. We consider basic algebraic properties of such chain complexes, including long-exact sequences associated to deletio…
We introduce the notion of the projective linking number Link(M,Z) of a compact oriented real submanifold M of dimension 2p-1 in complex projective n-space P^n with an algebraic subvariety Z in P^n - M of codimension p. This notion is related to projective winding numbers and quasi-plurisubharmonic functions, and it ge…
We focus on L-spaces for which the boundary maps of the Heegaard Floer chain complexes vanish. In previous paper \cite{Usui}, we collect such manifolds systematically by using the smoothing order on links. In this paper, we classify such L-spaces under appropreate constraint.
We develop the intersection theory at relative chain-cochain level, and apply it along with the use of Seifert disks for an oriented link to give a combinatorial algorithm to compute Massey's higher order linking numbers. It is subtle to compute higher-order linking numbers, and it has been a folklore to use the inters…
We define an annular concordance invariant and study its properties. When specialized to braids, this invariant gives bounds on band rank. We introduce a modified chain complex to reformulate the invariant. Then, by focusing on a special case, we give a refinement of the transverse invariant . We also study the …
In this thesis we work with Khovanov homology of links and its generalizations, as well as with the homology of graphs. Khovanov homology of links consists of graded chain complexes which are link invariants, up to chain homotopy, with graded Euler characteristic equal to the Jones polynomial of the link. Hence, it can…
New topological realization of Kontsevich graph complex for large dimensions.