New invariant measures knotted surfaces in 4D, revealing unknottedness.
problem Measuring knotted surfaces in 4D.
method Defined an integer invariant for bridge trisections of surfaces in or .
result Invariant implies the surface is unknotted.
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.
168,695 papers · 148 categories
Trend · papers per month
14 results for “Zupan”
In the paper we prove the conjecture by Alexander Zupan that where w denote the width and and are satellite knot and its companion with winding number . Also we proved that for satellite knot with braid pattern, the equality holds.
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.
Meier and Zupan showed that every surface in the four-sphere admits a bridge trisection and can therefore be represented by three simple tangles. This raises the possibility of applying methods from link homology to knotted surfaces. We use link homology to construct an invariant of knotted surfaces (up to isotopy) whi…
Confirming the Powell Conjecture for genus-3 Heegaard splittings of the 3-sphere.
problem Proving the finitely generated nature of the Goeritz group for genus-3 Heegaard splittings of the 3-sphere.
method Establishing the connectivity of reducing sphere complexes for the genus-3 case.
result Confirmation of the Powell Conjecture for genus-3 Heegaard splittings of the 3-sphere.
We generalize bridge trisections to surfaces in four-manifolds, linking them to braided links.
problem Embedding surfaces in four-manifolds and understanding their braiding.
method Introducing bridge trisections, isotoping surfaces, and using trisections and open-book decompositions.
result Any neatly embedded surface can be isotoped to lie in bridge trisection position with respect to any trisection of the four-manifold.
Study of 3-manifolds in 5-sphere using bridge decompositions.
problem Understanding embeddings of 3-manifolds in 5-sphere.
method Introduce and study bridge decompositions, use multisections of 5-manifolds.
result Every embedded 3-manifold admits a bridge decomposition.
In this paper, we study surfaces embedded in -manifolds. We give a complete set of moves relating banded unlink diagrams of isotopic surfaces in an arbitrary -manifold. This extends work of Swenton and Kearton-Kurlin in . As an application, we show that bridge trisections of isotopic surfaces in a trisected …
The paper calculates ribbon numbers for 12-crossing knots using Alexander polynomials.
problem Determining the minimum number of ribbon singularities for knots.
method Using Alexander polynomials and systematic treatment of knot invariants.
result Computed ribbon numbers for many 12-crossing knots.
The paper verifies stable handleslide triviality of some R-links and shows many are stably equivalent.
problem Stable handleslide triviality of R-links as potential counterexamples to the generalized property R conjecture.
method Implemented an algorithm to construct all R-links explicitly and verified their stable handleslide triviality.
result Many R-links are stably handleslide equivalent.
New methods find minimal crossing numbers for surfaces in .
problem Determining minimal crossing numbers for surfaces in .
method Developed new tri-plane diagrams to analyze surfaces.
result Proved minimal crossing numbers for nonorientable unknotted surfaces in .
New examples of knots with infinitely many inequivalent slice disks.
problem Existence of knots with infinitely many pairwise nonisotopic slice disks.
method Classification of fibered, homotopy-ribbon disks and use of satellite operations.
result Examples of fibered, hyperbolic knots bounding infinitely many fibered, ribbon disks that are pairwise nonisotopic modulo local knotting.
In this paper, we develop new techniques for understanding surfaces in via bridge trisections. Trisections are a novel approach to smooth 4-manifold topology, introduced by Gay and Kirby, that provide an avenue to apply 3-dimensional tools to 4-dimensional problems. Meier and Zupan subsequently develope…
New method shows certain group presentations are trivial.
problem Proving certain group presentations are trivial.
method 4-manifold trisections
result Certain group presentations are Andrews-Curtis trivial.