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Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 11/2017, Volume 26, Issue 13, p. 1750087
We note that a rational 3 -tangle diagram is obtained from a combination of four generators. There is an algorithm to distinguish two rational 3 -tangle... 
standard parameterization | Dehn parameterization | four generators of rational 3-tangle diagrams | Rational 3-tangle diagram | MATHEMATICS
Journal Article
Communications of the Korean Mathematical Society, ISSN 1225-1763, 2012, Volume 27, Issue 4, pp. 815 - 834
Journal Article
GAFA Geometric And Functional Analysis, ISSN 1016-443X, 12/2006, Volume 16, Issue 6, pp. 1324 - 1376
We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function n2log n. Some of these groups... 
20F10 | S -machine | Analysis | chord diagram | Dehn function | 20E07 | 20F06 | Mathematics | conjugacy problem | Conjugacy problem | S-machine | Chord diagram | MATHEMATICS
Journal Article
by Kwon, B
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 01/2015, Volume 24, Issue 1, pp. 1550004 - 1-1550004-62
A 3-tangle T is the disjoint union of three properly embedded arcs in the unit 3-ball; it is called rational if there is a homeomorphism of pairs from (B3, T)... 
hexagon diagram | Dehn parametrization | Rational 3-tangles | standard diagram | MATHEMATICS | TANGLES | CLASSIFICATION | Algorithms | Knot theory | Boundaries | Classification | Unions
Journal Article
Journal of Algebra, ISSN 0021-8693, 04/2018, Volume 500, pp. 193 - 220
We study the phenomenon in which commutation relations for sequences of elements in a ring are implied by similar relations for subsequences involving at most... 
Dehn diagram | Commutation relations | Elementary symmetric function | Rule of Three | Noncommutative symmetric function | MATHEMATICS
Journal Article
Journal of Algebra, ISSN 0021-8693, 04/2015, Volume 428, pp. 457 - 470
Guba [8] proved that the Dehn function of the Thompson group F is quadratic. In this paper, we apply his idea and extend his result to the generalized Thompson... 
Thompson's group | Dehn function | Van Kampen diagram | GROUP-F | MATHEMATICS | ISOPERIMETRIC-INEQUALITIES
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 02/2017, Volume 27, Issue 1, pp. 1 - 21
Let F(p), p >= 2 be the family of generalized Thompson's groups. Here, F(2) is the famous Richard Thompson's group usually denoted by F. We find the growth... 
Generalized Thompson's groups | growth | GROUP-F | MATHEMATICS | PIECEWISE LINEAR HOMEOMORPHISMS | DEHN FUNCTION | MINIMAL LENGTH ELEMENTS | DIAGRAM GROUPS
Journal Article
by Kang, S
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, ISSN 1015-8634, 01/2020, Volume 57, Issue 1, pp. 1 - 30
In this paper, we classify all twisted torus knots which are middle/hyper doubly Seifert. By the definition of middle/hyper doubly Seifert knots, these knots... 
graph manifolds | R-R diagrams | MATHEMATICS | middle/hyper doubly Seifert knots | Dehn surgery | twisted torus knots
Journal Article
Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, 10/2018, Volume 115, Issue 43, pp. 10887 - 10893
We summarize and expand known connections between the study of Dehn surgery on links and the study of trisections of closed, smooth 4-manifolds. In particular,... 
Generalized Property R Conjecture | Trisections | 4-manifolds | Dehn surgery | Heegaard splitting | Generalized Property | MULTIDISCIPLINARY SCIENCES | KNOTS | HEEGAARD-SPLITTINGS | CONJECTURE | DIAGRAMS | R Conjecture | 3-MANIFOLDS | trisections | STANDARD | Manifolds (Mathematics) | Research | Mathematical research | Decomposition (Mathematics) | Physical Sciences | 105 | 516
Journal Article
Mathematical Notes, ISSN 0001-4346, 8/2011, Volume 90, Issue 1, pp. 227 - 237
An invariant of links with two and more components in the thickened torus is constructed; the invariant depends on several variables. The construction uses... 
regular link diagram | virtual knot | Mathematics, general | Mathematics | invariant of links | link in the thickened torus | shadow of a link diagram | Kaufmann’s formal theory | Dehn’s presentation | link diagram | Kaufmann's formal theory | Dehn's presentation | MATHEMATICS | TEXTILE STRUCTURES
Journal Article
Journal of Geometry, ISSN 0047-2468, 12/2014, Volume 105, Issue 3, pp. 601 - 614
We study a series of 2-generator Sol-manifolds depending on a positive integer n, introduced by Molnár and Szirmai. We construct them as tetrahedron manifolds... 
Dehn surgery | link | 57M12 | Thurston geometries | branched covering | Mathematics | group presentation | 57M25 | Geometry | discrete group | Sol manifold | lattice | Heegaard diagram
Journal Article
Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2016, Volume 53, Issue 1, pp. 273 - 301
In this paper, we classify all twisted torus knots which are doubly middle Seifert-fibered. Also we show that all of these knots possibly except a few admit... 
R-R diagrams | Twisted torus knots | Graph manifolds | Seifert curves | Dehn surgery | Knots | graph manifolds | MATHEMATICS | twisted torus knots | knots
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 10/2018, Volume 18, Issue 6, pp. 3691 - 3718
A closed braid beta naturally gives rise to a transverse link K in the standard contact 3- space. We study the effect of the dynamical properties of the... 
MATHEMATICS | HEEGAARD FLOER HOMOLOGY | RASMUSSEN INVARIANT | RIGHT-VEERING DIFFEOMORPHISMS | COMPACT SURFACES | LEGENDRIAN KNOTS
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 04/2016, Volume 25, Issue 4, p. 1650018
We prove that any knot or link in any 3 -manifold can be nicely decomposed (split) by a filling Dehn sphere. This has interesting consequences in the study of... 
branched coverings | immersed surface | filling Dehn surface | 3-manifold | links | knots | Johansson diagrams | MATHEMATICS | LEMMA | COMPLEXITY | 3-MANIFOLDS | IMMERSED SURFACES | Algorithms
Journal Article
ALGEBRAIC AND GEOMETRIC TOPOLOGY, ISSN 1472-2739, 2003, Volume 3, Issue 1, pp. 235 - 285
The twisted face-pairing construction of our earlier papers gives an efficient way of generating, mechanically and with little effort, myriads of relatively... 
MATHEMATICS | Heegaard diagrams | Dehn surgery | 3-manifold constructions | Mathematics - Geometric Topology
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2001, Volume 129, Issue 2, pp. 559 - 566
We will give a very simple algorithm to decompose a gluing homeomorphism of a planar Heegaard diagram of genus two into Dehn twists associated with the... 
Homeomorphism | Dehn twist | Heegaard diagram | Dehn surgery | 2-bridge link | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
New York Journal of Mathematics, ISSN 1076-9803, 2002, Volume 8, pp. 169 - 179
Journal Article
Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 01/2011, Volume 48, Issue 1, pp. 197 - 211
Every (1, 1)-knot is represented by a 4-tuple of integers (a, b, c, r), where a > 0, b >= 0, c >= 0, d = 2a + b + c, r is an element of Z(d), and it is well... 
(1,1)-knot | Dunwoody manifold | Torus knot | Crystallization | (1,1)-decomposition | Heegaard diagram | 2-bridge knot | Cyclic branched covering | Heegaard splitting | DEHN SURGERIES | GENUS | cyclic branched covering | MATHEMATICS | torus knot | 2-FOLD BRANCHED-COVERINGS | crystallization | 1-BRIDGE KNOTS | CRYSTALLIZATIONS | SURFACES
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 12/1991, Volume 328, Issue 2, pp. 863 - 879
For a 3-manifold M(L) obtained by an integral Dehn surgery along an n-bridge link L with n-components we define a concept of planar Heegaard diagrams of M(L)... 
Integers | Traditional Chinese medicine | Mathematics | Mathematical theorems | Diagrams | 3-manifolds | Heegaard diagram | Dehn surgery | N-bridge link | MATHEMATICS | 3-MANIFOLDS | HEEGAARD DIAGRAM | DEHN SURGERY | N-BRIDGE LINK
Journal Article
Fundamenta Mathematicae, ISSN 0016-2736, 2006, Volume 190, pp. 245 - 288
A Dehn sphere Sigma in a closed 3-manifold M is a 2-sphere immersed in M with only double curve and triple point singularities. The Dehn sphere Sigma fills M... 
Immersed surfaces | Representation of 3-manifolds | Set of moves | Dehn surfaces | Triple points | Johansson diagram | Double curves | MATHEMATICS | DEHN LEMMA | triple points | double curves | immersed surfaces | POINTS | set of moves | representation of 3-manifolds
Journal Article
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