It is shown that any handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link up to equivalences, so that every stable-ribbon surface-link is a ribbon surface-link. This is a generalization of a previously observed result for a stably trivial surface-link. Two observations are give…
On-device research index
arXiv research
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.
168,657 papers · 148 categories
Trend · papers per month
48 results for “Surface links”
New concept of quasi-ribbon surface-links simplifies complex surface-links.
problem Complexity in surface-links of trivial components.
method Introducing quasi-ribbon surface-links as a generalization of ribbon surface-links.
result Every F-link of trivial components on a surface F with at most one aspheric component is a quasi-ribbon surface-link.
A new method for describing surface-links in 4-space.
problem Describing surface-links in 4-dimensional space.
method Introducing a plat form method using braided surfaces.
result Every surface-link can be described in a plat form.
We introduce the notion of a ribbon-clasp surface-link, which is a generalization of a ribbon surface-link. We generalize the notion of a normal form on embedded surface-links to the case of immersed surface-links and prove that any (immersed) surface-link can be described in a normal form. It is known that an embedded…
Free surface-links are shown to be ribbon links.
problem Characterizing surface-links as ribbon links.
method Four proofs are provided, including a stabilization approach.
result Every free surface-link is a ribbon surface-link.
Revised proof shows ribbonness of surface-links in 4-sphere.
problem Determining ribbonness of surface-links in 4-sphere.
method Surgery along fusion 1-handle systems to prove ribbonness.
result Surface-links in 4-sphere are ribbon if certain conditions are met.
For an oriented surface link , we can take a satellite construction called a 2-dimensional braid over , which is a surface link in the form of a covering over . We demonstrate that 2-dimensional braids over surface links are useful for showing the distinctness of surface links. We investigate non-trivial examp…
There is a question asking whether a handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link. This question for the case of a trivial surface-link is affirmatively answered. That is, a handle-irreducible summand of every stably trivial surface-link is only a trivial 2-link. By com…
New method finds infinitely many surface knots with specific bridge numbers.
problem Finding numerical invariants for surface links.
method Colorings of surface links by keis to prove bridge number existence.
result Existence of infinitely many surface knots with bridge number n for n ≥ 4.
We study surface links whose link groups are free abelian, and construct various stimulating and highly non-trivial examples of such surface links.
Enhanced bikei modules distinguish unoriented and non-orientable surface-links.
problem Distinguishing unoriented and non-orientable surface-links.
method Extending biquandle module invariants to unoriented surface-links using bikei modules.
result Enhanced bikei modules are more effective at distinguishing non-orientable surface-links than bikei homset cardinality alone.
Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface in…
The paper studies alternating links in thickened surfaces using flow lattices and disc mutations.
problem Understanding alternating links in thickened surfaces and their invariants.
method Using integer flows on Tait graphs and disc mutations, the paper proves invariants and compares link properties.
result Found alternating knots with isometric flow lattices but different linking forms.
This note proves properties of surface-links with trivial components.
problem Properties of surface-links with trivial components.
method Analyzes closed oriented disconnected surfaces and their links.
result For certain surface-links, trivial components result in ribbon links.
Extends Goldberg's result for string links over surfaces.
problem Generalized string links over surfaces.
method Extension of Goldberg's result.
result Exact sequence for generalized string links over surfaces.
Meridian lemma extended to fully alternating links in thickened surfaces.
problem Extending Menasco's meridian lemma to fully alternating links in thickened surfaces.
method Developed a new meridian lemma for fully alternating links in thickened orientable surfaces of positive genus.
result The meridian lemma holds for fully alternating links in thickened surfaces.
The paper studies right-angled links on higher genus surfaces.
problem Classifying and understanding right-angled links on surfaces of higher genus.
method Defining and proving equivalence of properties for RGCR links, using diagram restrictions and polygonal checkerboard surfaces.
result Classification of RGCR links and bounds on their number for a given genus.
Study of alternating links on nonorientable surfaces, extending results to nonorientable projections.
problem Generalizing hyperbolic geometry results to nonorientable surfaces.
method Extending results from orientable to nonorientable surfaces.
result Klein-bottly alternating links in prism manifolds have hyperbolic geometry.
In this paper, we formulate a construction of ideal coset invariants for surface-links in -space using invariants for knots and links in -space. We apply the construction to the Kauffman bracket polynomial invariant and obtain an invariant for surface-links called the Kauffman bracket ideal coset invariant of sur…
This paper shows how to create surface-links with many triple points.
problem Creating surface-links with a large number of triple points.
method Analogous to knot diagrams, the paper uses broken sheet diagrams to project surface-links and analyze their triple points.
result There are non-split surface-links with arbitrarily many triple points.
Computation of the knot symmetric quandle and its application to the plat index of surface-linksmath.GT
Paper computes knot symmetric quandle for surface-links and finds infinitely many distinct surface-knots.
problem Computing knot symmetric quandle for surface-links.
method Using plat form presentations, the paper computes the knot symmetric quandle for surface-links.
result Infinitely many distinct surface-knots of genus g with plat indices m.
Paper classifies surface-links using charts with specific properties.
problem Classifying surface-links with specific charts.
method Using quandle colorings to differentiate charts representing different surface-links.
result Charts in the second class represent different surface-links.
Extends Milnor invariants to surface-links using cut-diagrams.
problem Tackles invariants for surface-links in 4-space.
method Introduces cut-diagrams and groups associated to them.
result Yields concordance and link-homotopy invariants for surface-links.
We characterize the first Alexander Z[Z]-modules of ribbon surface-links in the 4-sphere fixing the number of components and the total genus, and then the first Alexander Z[Z]-modules of surface-links in the 4-sphere fixing the number of components. Using the result of ribbon torus-links, we also characterize the first…
New homotopy types defined for links in thickened surfaces with higher genus.
problem Defining stable homotopy types for links in surfaces with higher genus.
method Defined Khovanov-Lipshitz-Sarkar homotopy types and Steenrod squares for links in thickened surfaces with genus > 1.
result First meaningful Khovanov-Lipshitz-Sarkar stable homotopy types for links in 3-manifolds other than the 3-sphere.
Essential surfaces in link diagrams on surfaces are crucial for understanding link properties.
problem Understanding the essentiality of surfaces in link diagrams on surfaces.
method Proving checkerboard surfaces are π1-essential and contain no essential closed curves that are ∂-parallel.
result Checkerboard surfaces of alternating link diagrams are π1-essential and contain no essential closed curves that are ∂-parallel.
Marked Graph Mosaicsmath.GT
Enhances knot counting using mosaic diagrams.
problem Counting and classifying surface-links and knots.
method Marked graph diagrams and mosaic numbers.
result Established bounds on mosaic numbers for surface-links.
Study links' flat-virtual diagrams to create link invariants.
problem Equivalence and invariants of flat-virtual diagrams.
method Maps from links in thickened surfaces to flat-virtual links.
result Investigation of flat-virtual diagrams' equivalence and invariants.
Totally geodesic surfaces found in knots and links.
problem Finding totally geodesic surfaces in knots and links.
method Constructing infinite families of knots and links with totally geodesic spanning surfaces in various 3-manifolds.
result Infinite families of knots and links with totally geodesic spanning surfaces in multiple 3-manifolds.
The paper constructs exotic surface links in 4-ball, proving their Brunnian nature.
problem Investigating exotic surface links in 4-ball.
method Two constructions of Brunnian exotic surface links, using satellite operations and covering links.
result Provided constructions of exotic Brunnian surface links with varied properties.
Proves certain alternating links have specific geometric properties.
problem Characterizing alternating links with totally geodesic checkerboard surfaces.
method Analyzes links with two totally geodesic checkerboard surfaces and characterizes them.
result Proves links with two totally geodesic checkerboard surfaces are three specific links.
State Surfaces of Linksmath.GT
State surfaces are spanning surfaces of links that are obtained from link diagrams guided by the combinatorics underlying Kauffman's construction of the Jones polynomial via state models. Geometric properties of such surfaces are often dictated by simple link diagrammatic criteria, and the surfaces themselves carry imp…
Every link is shown to be presentable as a boundary of an unknotted flat banded surface. A (flat) banded link is defined as a boundary of an unknotted (flat) banded surface. A link's (flat) band index is defined as the minimum number of bands required to present the link as boundaries of an unknotted (flat) banded surf…
New tool lassos connects virtual and surface link diagrams, changing primeness rules.
problem Establishing a new correspondence between virtual and surface link diagrams.
method Using a new tool called lassos, establishing a new correspondence between cellular link diagrams on closed surfaces and equivalence classes of virtual link diagrams.
result Traditional primeness for virtual links is stricter than for links in thickened surfaces.
It is proved that every disconnected surface-link with meridian-based free fundamental group is a trivial (i.e., an unknotted-unlinked) surface-link. This result is a surface-link version of the author's recent announcement result on smooth unknotting of a surface-knot.
Characterizes knot groups and symmetric quandles of surface-links.
problem Characterize knot groups and symmetric quandles of surface-links.
method Used plat presentations for surface-links and closed 2-dimensional braids.
result Generalized results to include non-orientable surface-links and showed that dihedral quandles can be realized as symmetric quandles of surface-links.
Standard position for surfaces extended to weakly generalized alternating links.
problem Proving standard position for surfaces in a broader class of links.
method Extending techniques from classical alternating links to weakly generalized alternating links.
result All weakly generalized alternating links are prime, and Conway spheres interact with diagrams as in classical setting.
We prove a Kauffman-Murasugi-Thistlethwaite theorem for alternating links in thickened surfaces. It states that any reduced alternating diagram of a link in a thickened surface has minimal crossing number, and any two reduced alternating diagrams of the same link have the same writhe. This result is proved more general…
New theorem bounds link volume using surface coefficients.
problem Bounding hyperbolic volume of links on surfaces.
method Analogue of Dasbach-Lin theorem for surface links.
result Bounds on link volume from surface polynomial coefficients.
We introduce the notion of a quandle with a good involution and its homology groups. Carter et al. defined quandle cocycle invariants for oriented links and oriented surface-links. By use of good involutions, quandle cocyle invariants can be defined for links and surface-links which are not necessarily oriented or orie…
Proves a plumbing-multiplicative property of a Links-Gould invariant.
problem Proving a multiplicative property of the Links-Gould invariant.
method Using Laurent polynomials and topological plumbing of surfaces.
result The Links-Gould invariant is monic in the Laurent polynomial ring.
The paper studies knitted surfaces and surface-links, showing their isotopy and closure properties.
problem Understanding the isotopy and closure properties of knitted surfaces and surface-links.
method Analyzing the structure and closure of knitted surfaces and surface-links in .
result Any surface-link is ambient isotopic to the closure of a 2-dimensional knit.
Same-genus Seifert surfaces for non-split alternating links are smoothly isotopic.
problem Understanding the uniqueness of Seifert surfaces for non-split alternating links.
method Analyzing the smooth isotopy of Seifert surfaces in the 4-ball.
result Same-genus Seifert surfaces for non-split alternating links are smoothly isotopic.
Characterizes arithmetic and commensurable links in curved surfaces.
problem Classifying arithmetic and commensurable links in curved surfaces.
method Combines symmetry arguments, combinatorial geometry, and number-theoretic data.
result Characterizes arithmetic and commensurable right-angled tiling links.
By using the cohomology theory of quandles, quandle cocycle invariants and shadow quandle cocycle invariants are defined for oriented links and surface-links via broken surface diagrams. By using symmetric quandles, symmetric quandle cocycle invariants are also defined for unoriented links and surface-links via broken …
It is well known that surface-links in 4-space can be presented by diagrams on the plane of 4-valent spatial graphs with makers on the vertices, called marked graph diagrams. In this paper we extend the method of presenting surface-links by marked graph diagrams to presenting immersed surface-links. We also give some m…
Upper bounds for surface-links in the Yoshikawa table are estimated.
problem Estimating Kirby-Thompson invariants of surface-links.
method Using tri-plane diagrams and L-, L*-invariants.
result Upper bounds for surface-links in the Yoshikawa table are obtained.
In-degree quiver polynomials for surface-links computed.
problem Computing in-degree quiver polynomials for surface-links.
method Defined using a quandle and set of endomorphisms, computed for surface-links with ch-index up to 10.
result Example computations for surface-links with ch-index up to 10.