相关论文: Triple linking numbers and surface systems
Given a rational homology 3-sphere $M$, we introduce a triple linking form on $H_1(M; \mathbb{Z})$, defined when the classical torsion linking pairing of three homology classes vanishes pairwise. If $M$ is the boundary of a simply-connected…
We prove the meridional rank conjecture for twisted links and arborescent links associated to bipartite trees with even weights. These links are substantial generalizations of pretzels and two-bridge links, respectively. Lower bounds on…
We analyze the orbifolds that can be obtained as quotients of hyperbolic 3-manifolds admitting a Heegaard splitting of genus two by their orientation preserving isometry groups. The genus two hyperbolic 3-manifolds are exactly the…
In his Ph.D. thesis, Cadegan-Schlieper constructs an invariant of the embedded topology of a line arrangement which generalizes the $\mathcal{I}$-invariant introduced by Artal, Florens and the author. This new invariant is called the loop…
We consider the class of dispersing billiard systems in the plane formed by removing three convex analytic scatterers satisfying the non-eclipse condition. The collision map in this system is conjugated to a subshift, providing a natural…
We study relations between cluster algebra invariants and link invariants. First, we show that several constructions of positroid links (permutation links, Richardson links, grid diagram links, plabic graph links) give rise to isotopic…
The theory of signature invariants of links in rational homology spheres is applied to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, an explicit formula is derived to compute…
This paper defines a new sequence of finite dimensional algebras as quotients of the group algebras of the braid groups. This sequence depends on three homogeneous parameters and has a one-parameter family of Markov traces, and so gives a…
Various integrals over elliptic integrals are evaluated as couplings on spheres, resulting in some integral and series representations for the mathematical constants $\pi$, $G$ and $\zeta(3)$.
We announce results about flat (linkless) embeddings of graphs in 3-space. A piecewise-linear embedding of a graph in 3-space is called {\it flat} if every circuit of the graph bounds a disk disjoint from the rest of the graph. We have…
The Alexander polynomial in several variables is defined for links in three-dimensional homology spheres, in particular, in the Poincar\'e sphere: the intersection of the surface $S=\{(z_1,z_2,z_3)\in {\mathbb C}^3: z_1^5+z_2^3+z_3^2=0\}$…
We show how in principle a coherent coupling between two superconductors of opposite parity can be realized in a three-layer oxide heterostructure. Due to strong intraionic spin-orbit coupling in the middle layer, singlet Cooper pairs are…
We define the {\it Wirtinger number} of a link, an invariant closely related to the meridional rank. The Wirtinger number is the minimum number of generators of the fundamental group of the link complement over all meridional presentations…
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…
We obtain Polyak-Viro type formula for the Milnor triple linking number that can be applied to diagrams with triple or more multiple-crossings. The proof is based on the idea of Brooks and Komendarczyk, but is different from theirs in that…
Three band crossings can arise in three dimensional quantum materials with certain space group symmetries. The low energy Hamiltonian supports spin $\textit{one}$ fermions and a flat band. We study the pairing problem in this setting. We…
Let W be a planar 3-web defined on a neighborhood of a point M. We call "symmetry of W around M" any local diffeomorphism which fixes M and maps each foliation of W to a (not necessarily the same) foliation of W. We say that it is a simple…
We study the relation between the set of oriented $\mathbb{Z}/d$-homology $3$-spheres and the level-$d$ mapping class groups, the kernels of the canonical maps from the mapping class group of an oriented surface to the symplectic group with…
In the article The third homology of $SL_{2}(\mathbb{Q})$, Hutchinson determined the structure of $H_{3}\left(\mathrm{SL}_{2}(\mathbb{Q}),\mathbb{Z}\left[\frac{1}{2}\right]\right)$ by expressing it in terms of…
In this paper, we characterize all links in the 3-sphere with bridge number at least three that have a bridge sphere of distance two. We show that a link L has a bridge sphere of distance at most two then it falls into at least one of three…