7 papers
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…
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,…
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…
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…