Results 11 to 20 of about 6,627,879 (323)
Journal of Knot Theory and Its RamificationsIn this paper, we generalize virtual knot theory to multi-virtual knot theory where there are a multiplicity of virtual crossings. Each virtual crossing type can detour over the other virtual crossing types, and over classical or immersed crossings. New invariants of multi-virtual knots and links are introduced and new problems that arise are described.
Louis H. Kauffman
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Introduction to disoriented knot theory [PDF]
Open Mathematics, 2018 This paper is an introduction to disoriented knot theory, which is a generalization of the oriented knot and link diagrams and an exposition of new ideas and constructions, including the basic definitions and concepts such as disoriented knot ...
Altıntaş İsmet
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Khovanov Laplacian and Khovanov Dirac for knots and links [PDF]
Journal of Physics: ComplexityKhovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000. This work introduces a Khovanov Laplacian and a Khovanov Dirac to study knot and link diagrams.
Benjamin Jones, Guo-Wei Wei
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THE TRIESTE LOOK AT KNOT THEORY [PDF]
, 2011 41 pages, 46 figures, Chapter in the book "Introductory Lectures on Knot Theory: Selected Lectures presented at the Advanced School and Conference on Knot Theory and its Applications to Physics and Biology", ICTP, Trieste, Italy, 11 - 29 May 2009, World Scientific, to appear ...
J. Przytycki
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Delta-groupoids in knot theory [PDF]
Geom. Dedicata, 2009 A Delta-groupoid is an algebraic structure which axiomitizes the combinatorics of a truncated tetrahedron. It is shown that there are relations of Delta-groupoids to rings, group pairs, and (ideal) triangulations of three-manifolds. In particular, one can associate a Delta-groupoid to ideal triangulations of knot complements.
Kashaev, Rinat Mavlyavievich
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New Directions in Geometric and Applied Knot Theory [PDF]
, 2022 The aim of this book is to present recent results in both theoretical and applied knot theory—which are at the same time stimulating for leading researchers in the field as well as accessible to non-experts.
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Knot theory and cluster algebras [PDF]
Advances in Mathematics, 2021 We establish a connection between knot theory and cluster algebras via representation theory. To every knot diagram (or link diagram), we associate a cluster algebra by constructing a quiver with potential. The rank of the cluster algebra is $2n$, where $
V'eronique Bazier-Matte, R. Schiffler
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An introduction to Thompson knot theory and to Jones subgroups [PDF]
Journal of knot theory and its ramifications, 2022 We review a constructions of knots from elements of the Thompson groups due to Vaughan Jones, which comes in two flavours: oriented and unoriented.
Valeriano Aiello
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Sensors, 2023 Manipulating cloth-like deformable objects (CDOs) is a long-standing problem in the robotics community. CDOs are flexible (non-rigid) objects that do not show a detectable level of compression strength while two points on the article are pushed towards ...
Halid Abdulrahim Kadi, Kasim Terzić
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KNOT THEORY IN HANDLEBODIES [PDF]
Journal of Knot Theory and Its Ramifications, 2002 We consider oriented knots and links in a handlebody of genus g through appropriate braid representatives in S3, which are elements of the braid groups Bg,n. We prove a geometric version of the Markov theorem for braid equivalence in the handlebody, which is based on the L-moves.
Oldenburg, Reinhard, Lambropoulou, Sofia
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