Daniele Celoria

University of Melbourne

Author Statistics

Papers

Citation

H-Index

i-10 index

Research Trends

Author Order

Document Type

Co-Authors

Agnese Barbensi

University of Melbourne

Carlo Collari

University of Pisa

Luigi Caputi

University of Aberdeen

Marco Golla

Centre National de la Recherche Scientifique

Dorothy Buck

Duke University

Heather A. Harrington

University of Oxford

Andrzej Stasiak

University of Lausanne

Antonio Alfieri

University of British Columbia

Naya Yerolemou

University of Oxford

András I. Stipsicz

Alfréd Rényi Institute of Mathematics

Cooperative Institutions

University of Oxford

Alfréd Rényi Institute of Mathematics

Mathematical Institute of the Slovak Academy of Sciences

Max Planck Institute for Mathematics

Hungarian Academy of Sciences

The Alan Turing Institute

Turing Institute

University of Trento

University of Pisa

Duke University

Author Statistics

Papers

Citation

H-Index

i-10 index

Research Field

Categorifying connected domination via graph überhomology

arXiv (Cornell University) (2022)

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 überhomology, is related to dominating sets in graphs. To this end, we interpret überhomology as a poset homology, and investigate its functoriality properties. We then show that the Euler characteristic of the bold homology of a graph coincides with an evaluation of its connected domination polynomial. Even more, the bold chain complex retracts onto a complex generated by connected dominating sets. We conclude with several computations of this homology on families of graphs; these include a vanishing result for trees, and a characterisation result for complete graphs.

10.48550/arxiv.2201.00721

Cite

Citations (0)

Rational cobordisms and integral homology

Compositio Mathematica (2020)

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 class in the subgroup generated by lens spaces is represented by a unique connected sum of lens spaces whose first homology group injects in the first homology group of any other element in the same class. As a first consequence, we show that several natural maps to the rational homology cobordism group have infinite-rank cokernels. Further consequences include a divisibility condition between the determinants of a connected sum of $2$ -bridge knots and any other knot in the same concordance class. Lastly, we use knot Floer homology combined with our main result to obstruct Dehn surgeries on knots from being rationally cobordant to lens spaces.

Lens space

Cobordism

Homology

Floer Homology

Connected sum

Khovanov homology

Relative homology

Morse homology

10.1112/s0010437x20007320

Cite

Citations (8)

On concordances in 3-manifolds

Journal of Topology (2018)

Daniele Celoria

We describe an action of the concordance group of knots in S 3 on concordances of knots in arbitrary 3-manifolds. As an application we define the notion of almost-concordance between knots. After some basic results, we prove the existence of non-trivial almost-concordance classes in all non-abelian 3-manifolds. Afterwards, we focus the attention on the case of lens spaces, and use a modified version of the Ozsváth–Szabó–Rasmussen's τ-invariant to obstruct almost-concordances and prove that each L ( p , 1 ) admits infinitely many nullhomologous non almost-concordant knots. Finally we prove an inequality involving the cobordism P L -genus of a knot and its τ-invariants, in the spirit of [Sarkar, Math. Res. Lett. 18 (2011) 1239–1257].

Cobordism

Concordance

Connected sum

10.1112/topo.12051

Cite

Citations (13)

A note on Grid Homology in lens spaces: $\mathbb{Z}$ coefficients and computations

arXiv (Cornell University) (2015)

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 $\partial_\mathbb{Z}^2 = 0$. We also present a Sage program that computes $\widehat{GH} (L(p,q),K;\mathbb{Z})$, and provide empirical evidence supporting the absence of torsion in these groups.

Homology

Through-the-lens metering

Source

Cite

Citations (0)

Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology

arXiv (Cornell University) (2019)

Agnese Barbensi Daniele Celoria Heather A. Harrington Andrzej Stasiak Dorothy Buck

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 these 2D diagrams can be used to model a complex 3D process such as the topoisomerase-mediated preferential unknotting of DNA molecules. We model here topoisomerase-mediated passages of double-stranded DNA segments through each other using the formalism of grid diagrams. We show that this grid diagram-based modelling approach captures the essence of the preferential unknotting mechanism, based on topoisomerase selectivity of hooked DNA juxtapositions as the sites of intersegmental passages. We show that grid diagram-based approach provide an important, new and computationally convenient framework for investigating entanglement in biopolymers.

Formalism (music)

10.48550/arxiv.1909.05937

Cite

Citations (0)

A statistical approach to knot confinement via persistent homology

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences (2022)

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 metric neighbourhood of a knot's embedding for growing radii. Specifically, we extract features from the persistent homology (PH) of the Vietoris-Rips complexes built from point clouds associated with knots. Statistical analysis of our data shows the existence of increasing correlations between geometric quantities associated with the embedding and PH-based features, as a function of the knots' lengths. We further study the variation of these correlations for different knot types. Finally, this framework also allows us to define a simple notion of deviation from ideal configurations of knots.

Persistent Homology

Topological data analysis

Homology

10.1098/rspa.2021.0709

Cite

Citations (3)

Filtered matchings and simplicial complexes

arXiv (Cornell University) (2020)

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 construction leads to the definition of several homology theories, which we compute in a number of examples. We also completely determine the graded object associated to this filtration in terms of the homology of simpler complexes. This last result provides some connections to the number of vertex-disjoint cycles of a graph.

Simplicial homology

Disjoint sets

Homology

Simplicial approximation theorem

Filtration (mathematics)

Abstract simplicial complex

Discrete Morse theory

10.48550/arxiv.2011.02015

Cite

Citations (3)

Knot intensity distribution: a local measure of entanglement

arXiv (Cornell University) (2022)

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 focusing on an exact determination, we introduce the knot intensity distribution, a local quantifier for the contribution of a curve's region to global entanglement. The integral of the distribution yields a measure of tightness for knots. We compute the distribution for ideal knots, and study its behaviour on prime and composite random knots. Intensity distributions provide an effective method to locate entanglement. In particular, they identify regions in knots that accommodate passages leading to topological changes.

Intensity

10.48550/arxiv.2211.12069

Cite

Citations (1)

Heegaard Floer homology and concordance bounds on the Thurston norm

Transactions of the American Mathematical Society (2019)

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 of a 2 2 -component link L L in S 3 S^3 . We then specialise this procedure to knots in S 2 × S 1 S^2 \times S^1 and obtain a lower bound on their geometric winding number. We then provide an infinite family of null-homologous knots with increasing geometric winding number on which the bound is sharp.

Floer Homology

Concordance

Homology

10.1090/tran/7906

Cite

Citations (2)

A Discrete Morse Perspective on Knot Projections and a Generalised Clock Theorem

The Electronic Journal of Combinatorics (2021)

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 the two sphere, extending a construction due to Cohen. We show these dMfs are in bijection with certain rooted spanning forests in the Tait graph. We use this to count the number of such dMfs with a closed formula involving the graph Laplacian. We then simultaneously generalise Kauffman's Clock Theorem and Kenyon-Propp-Wilson's correspondence in two different directions; we first prove that the image of the correspondence induces a bijection on perfect dMfs, then we show that all perfect matchings, subject to an admissibility condition, are related by a finite sequence of click and clock moves. Finally, we study and compare the matching and discrete Morse complexes associated to the Tait graph, in terms of partial Kauffman states, and provide some computations.

10.37236/9979

Cite

Citations (0)