24 citations · 81 across the 19 of their papers we have counts for
20 papers
An exploration of low crossing and chiral cosmetic bands with grid diagrams
Agnese Barbensi, Daniele Celoria, Christopher Ktenidis +3
We computationally explore non-coherent band attachments between low crossing number knots, using grid diagrams. We significantly improve the current H(2)-distance table. In partic…
Bridging between überhomology and double homology
Luigi Caputi, Daniele Celoria, Carlo Collari
We establish an isomorphism between the 0-degree überhomology and the double homology of finite simplicial complexes, using a Mayer-Vietoris spectral sequence argument. We clarify…
From the Mayer-Vietoris spectral sequence to überhomology
Luigi Caputi, Daniele Celoria, Carlo Collari
We prove that the second page of the Mayer-Vietoris spectral sequence, with respect to anti-star covers, can be identified with another homological invariant of simplicial complexe…
Knot intensity distribution: a local measure of entanglement
Agnese Barbensi, Daniele Celoria
The problem of finding robust and effective methods for locating entanglement in embedded curves is relevant to both applications and theoretical investigations. Rather than focusi…
GridPyM: a Python module to handle grid diagrams
Agnese Barbensi, Daniele Celoria
Grid diagrams are a combinatorial version of classical link diagrams, widely used in theoretical, computational and applied knot theory. Motivated by questions from (bio)-physical…
Monotone cohomologies and oriented matchings
Luigi Caputi, Daniele Celoria, Carlo Collari
In this paper, we extend the definition of cohomology associated to monotone graph properties, to encompass twisted functor coefficients. We introduce oriented matchings on graphs,…
Categorifying connected domination via graph überhomology
Luigi Caputi, Daniele Celoria, Carlo Collari
Überhomology is a recently defined homology theory for simplicial complexes, which yields subtle information on graphs. We prove that bold homology, a certain specialisation of übe…
A statistical approach to knot confinement via persistent homology
Daniele Celoria, Barbara I. Mahler
In this paper we study how randomly generated knots occupy a volume of space using topological methods. To this end, we consider the evolution of the first homology of an immersed…
Filtered simplicial homology, graph dissimilarity and überhomology
Daniele Celoria
We introduce a filtration on the simplicial homology of a finite simplicial complex X using bi-colourings of its vertices. This yields two dual homology theories closely related to…
Filtered matchings and simplicial complexes
Daniele Celoria, Naya Yerolemou
To any finite simplicial complex X, we associate a natural filtration starting from Chari and Joswig's discrete Morse complex and abutting to the matching complex of X. This constr…
A discrete Morse perspective on knot projections and a generalised clock theorem
Daniele Celoria, Naya Yerolemou
We obtain a simple and complete characterisation of which matchings on the Tait graph of a knot diagram induce a discrete Morse function (dMf) on , extending a construction du…
Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology
Agnese Barbensi, Daniele Celoria, Heather A. Harrington +2
Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether…
Rational cobordisms and integral homology
Paolo Aceto, Daniele Celoria, JungHwan Park
We consider the question of when a rational homology 3-sphere is rational homology cobordant to a connected sum of lens spaces. We prove that every rational homology cobordism clas…
Upsilon invariants from cyclic branched covers
Antonio Alfieri, Daniele Celoria, Andras Stipsicz
We extend the construction of upsilon-type invariants to null-homologous knots in rational homology three-spheres. By considering -fold cyclic branched covers with a prime p…
Heegaard Floer homology and concordance bounds on the Thurston norm
Daniele Celoria, Marco Golla
We prove that twisted correction terms in Heegaard Floer homology provide lower bounds on the Thurston norm of certain cohomology classes determined by the strong concordance class…
The Reidemeister graph is a complete knot invariant
Agnese Barbensi, Daniele Celoria
We describe two locally finite graphs naturally associated to each knot type K, called Reidemeister graphs. We determine several local and global properties of these graphs and pro…
On concordances in 3-manifolds
Daniele Celoria
We describe an action of the concordance group of knots in the three-sphere on concordances of knots in arbitrary 3-manifolds. As an application we define the notion of almost-conc…
A note on Grid Homology in lens spaces: coefficients and computations
Daniele Celoria
We present a combinatorial proof for the existence of the sign refined grid homology in lens spaces, and a self contained proof that . We also present…
A note on cobordisms of algebraic knots
József Bodnár, Daniele Celoria, Marco Golla
In this note we use Heegaard Floer homology to study smooth cobordisms of algebraic knots and complex deformations of cusp singularities of curves. The main tool will be the concor…
Cuspidal curves and Heegaard Floer homology
József Bodnár, Daniele Celoria, Marco Golla
We give bounds on the gap functions of the singularities of a cuspidal plane curve of arbitrary genus, generalising recent work of Borodzik and Livingston. We apply these inequalit…