Results 81 to 90 of about 28,962 (144)
A universal finite‐type invariant of knots in homology 3‐spheres
Journal of Topology, Volume 18, Issue 3, September 2025.Abstract An essential goal in the study of finite‐type invariants of some objects (knots, manifolds) is the construction of a universal finite‐type invariant, universal in the sense that it contains all finite‐type invariants of the given objects. Such a universal finite‐type invariant is known for knots in the 3‐sphere — the Kontsevich integral — and ...
Benjamin Audoux, Delphine Moussard
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Legendrian non‐isotopic unit conormal bundles in high dimensions
Journal of Topology, Volume 18, Issue 3, September 2025.Abstract For any compact connected submanifold K$K$ of Rn$\mathbb {R}^n$, let ΛK$\Lambda _K$ denote its unit conormal bundle, which is a Legendrian submanifold of the unit cotangent bundle of Rn$\mathbb {R}^n$. In this paper, we give examples of pairs (K0,K1)$(K_0,K_1)$ of compact connected submanifolds of Rn$\mathbb {R}^n$ such that ΛK0$\Lambda _{K_0}$
Yukihiro Okamoto
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Edge‐Connectivity Between Edge‐Ends of Infinite Graphs
Journal of Graph Theory, Volume 109, Issue 4, Page 454-465, August 2025.ABSTRACT In infinite graph theory, the notion of ends, first introduced by Freudenthal and Jung for locally finite graphs, plays an important role when generalizing statements from finite graphs to infinite ones. Nash‐Williams' Tree‐Packing Theorem and MacLane's Planarity Criteria are examples of results that allow a topological approach, in which ends
Leandro Aurichi, Lucas Real
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Perturbative renormalisation for not-quite-connected bialgebras
, 2014 We observe that the Connes--Kreimer Hopf-algebraic approach to perturbative renormalisation works not just for Hopf algebras but more generally for filtered bialgebras $B$ with the property that $B_0$ is spanned by group-like elements (e.g.
Kock, Joachim
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Combinatorial Hopf algebra for interconnected nonlinear systems
, 2018 A detailed expose of the Hopf algebra approach to interconnected input-output systems in nonlinear control theory is presented. The focus is on input-output systems that can been represented in terms of Chen-Fliess functional expansions or Fliess operators. This provides a starting point for a discrete-time version of this theory.
Espinosa, Luis A. Duffaut +2 more
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 11630-11651, August 2025.ABSTRACT This study examines the complex dynamics of dengue transmission by incorporating time delay into a comprehensive model. The model is designed to capture several essential components, including steady‐state events, immune waning, recuperation from infection, and partial shielding in human populations.
G. M. Vijayalakshmi +4 more
wiley +1 more source
Coloring Complexes and Combinatorial Hopf Monoids
, 2021 We generalize the notion of coloring complex of a graph to linearized combinatorial Hopf monoids. These are a generalization of the notion of coloring complex of a graph. We determine when a combinatorial Hopf monoid has such a construction, and discover
White, Jacob
core
A combinatorial Hopf algebra on partition diagrams
Communications in AlgebraWe introduce a Combinatorial Hopf Algebra (CHA) with bases indexed by the partition diagrams indexing the bases for partition algebras. By analogy with the operation $H_α H_β = H_{α\cdot β}$ for the complete homogeneous basis of the CHA $ \textsf{NSym}$ given by concatenating compositions $α$ and $β$, we mimic this multiplication rule by setting ...
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Translations of rough paths in combinatorial Hopf algebras
, 2021 We generalize Bruned et.al.'s notion of translation in geometric and branched rough paths to a notion of translation in rough paths over any combinatorial Hopf algebra. We show that this notion of translation is equivalent to two bialgebras being in cointeraction, subject to certain additional conditions.
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