Results 1 to 10 of about 120,659 (273)

Unsolved Problems in Virtual Knot Theory and Combinatorial Knot Theory [PDF]

Banach Center Publications, 2014
This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.Comment: 65 pages, 24 figures.
Fenn, Roger, Ilyutko, Denis P., Kauffman, Louis H., Manturov, Vassily O.   +3 more
core   +2 more sources

Noncommutative knot theory [PDF]

Algebraic & Geometric Topology, 2004
The classical abelian invariants of a knot are the Alexander module, which is the first homology group of the the unique infinite cyclic covering space of S^3-K, considered as a module over the (commutative) Laurent polynomial ring, and the Blanchfield ...
Atiyah, Boileau, Brown, Cheeger, Cochran, Cohn, Cohn, Gordon, Hempel, Hillman, Hilton, Jacobson, Kawauchi, Kronheimer, Passman, Ranicki, Stallings, Stenström, Strebel, Tim D Cochran, Wall, Whitehead   +21 more
core   +5 more sources

Deep learning the hyperbolic volume of a knot

Physics Letters B, 2019
An important conjecture in knot theory relates the large-N, double scaling limit of the colored Jones polynomial JK,N(q) of a knot K to the hyperbolic volume of the knot complement, Vol(K).
Vishnu Jejjala, Arjun Kar, Onkar Parrikar   +2 more
doaj   +3 more sources

Khovanov Laplacian and Khovanov Dirac for knots and links [PDF]

Journal of Physics: Complexity
Khovanov 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
doaj   +2 more sources

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.
Kashaev, R. M.
core   +4 more sources

Classical Knot Theory

Symmetry, 2012
This paper is a very brief introduction to knot theory. It describes knot coloring by quandles, the fundamental group of a knot complement, and handle-decompositions of knot complements.
exaly   +3 more sources

Knot theory realizations in nematic colloids. [PDF]

Proc Natl Acad Sci U S A, 2015
Čopar S, Tkalec U, Muševič I, Žumer S.   +3 more
europepmc   +2 more sources

Knot theory and error-correcting codes. [PDF]

Des Codes Cryptogr
Kılıç AB, Nijsten A, Pellikaan R, Ravagnani A.   +3 more
europepmc   +2 more sources

Data-Driven Robotic Manipulation of Cloth-like Deformable Objects: The Present, Challenges and Future Prospects

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
doaj   +1 more source

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
openaire   +5 more sources