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Discrete & Computational Geometry, ISSN 0179-5376, 3/2018, Volume 59, Issue 2, pp. 331 - 362
...Discrete Comput Geom (2018) 59:331–362 https://doi.org/10.1007/s00454-017-9952-1 Graphs in the 3-Sphere with Maximum Symmetry Chao Wang 1 · Shicheng Wang 2... 
57M60 | Computational Mathematics and Numerical Analysis | Mathematics | Extendable action | 57M15 | 05E18 | Symmetry of 3-sphere | Combinatorics | Symmetry of graph | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | SURFACES | Graphs
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 08/2013, Volume 54, Issue 8, p. 82103
The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We present a special parametrization of the ellipto-spheroidal coordinate system suitable for the separation of variables... 
PHYSICS, MATHEMATICAL | SPHERICAL GEOMETRY | DYNAMICAL SYMMETRIES | Coulomb friction | Mathematical analysis | Quantum mechanics | Eigenvalues | Mathematical models | Polynomials | Wave functions | Vectors (mathematics) | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | SPHERES | EQUATIONS | EIGENFUNCTIONS | QUANTUM MECHANICS | WAVE FUNCTIONS | POLYNOMIALS | EIGENVALUES | QUANTIZATION | SPECTRA | COORDINATES | VECTORS | MATHEMATICAL METHODS AND COMPUTING
Journal Article
Regular and Chaotic Dynamics, ISSN 1560-3547, 7/2019, Volume 24, Issue 4, pp. 370 - 391
.... It suffices to consider the case when the sphere is 3-dimensional. As the 3-sphere is a group it acts on itself by left and right multiplication and these together generate the action of the SO... 
relative equilibria | 2-body problem | 53D20 | Mathematics | Dynamical Systems and Ergodic Theory | Lagrange top | reduction | 70F05 | MATHEMATICS, APPLIED | MECHANICS | SPACES | EQUATIONS | CLASSIFICATION | LIE | PHYSICS, MATHEMATICAL | SEMIDIRECT PRODUCTS | Mathematics - Dynamical Systems
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 2009, Volume 27, Issue 2, pp. 307 - 319
Let G ⊂ O ( 4 ) act isometrically on S 3 . In this article we calculate a lower bound for the diameter of the quotient spaces S 3 / G . We find it to be 1 2... 
TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | MANIFOLDS | SYMMETRY | CURVATURE
Journal Article
Topology and its applications, ISSN 0166-8641, 06/2020, p. 107313
Journal Article
Commentarii mathematici Helvetici, ISSN 0010-2571, 2005, Volume 80, Issue 2, pp. 317 - 354
The topological symmetry group of a graph embedded in the $3$-sphere is the group consisting of those automorphisms of the graph which are induced by some... 
General | Mechanics of deformable solids | Combinatorics | Global analysis, analysis on manifolds | Spatial graph | Embedded graph | Topological symmetry group | 3-connected graph | Automorphism group | MATHEMATICS | AUTOMORPHISMS | KNOTS | PERIOD
Journal Article
数学学报:英文版, ISSN 1439-8516, 2016, Volume 32, Issue 1, pp. 54 - 68
... ) for all possible embeddings Σg null → S 3 , where g>1. Keywords Symmetry of surface, symmetry of 3-sphere, extendable action MR(2010) Subject Classification 57M60, 57S17, 57S25... 
S3 | 有限群 | 订单 | 表面 | 动作 | 57M60 | 57S25 | 57S17 | extendable action | Mathematics, general | Mathematics | Symmetry of surface | symmetry of 3-sphere | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Topology and its Applications, ISSN 0166-8641, 10/2013, Volume 160, Issue 16, pp. 2088 - 2103
Journal Article
Tokyo journal of mathematics, ISSN 0387-3870, 2016, Volume 39, Issue 1, pp. 133 - 156
The symmetries of complex molecular structures can be modeled by the topological symmetry group of the underlying embedded graph. It is therefore important to... 
Spatial graphs | Topological symmetry groups | MATHEMATICS | 3-SPHERE | spatial graphs | topological symmetry groups
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 12/2014, Volume 23, Issue 14, pp. 1450077 - 1-1450077-13
We classify all groups which can occur as the orientation preserving topological symmetry group of some embedding of a Möbius ladder graph in S3. 
spatial graph | Topological symmetry group | molecular symmetries | Möbius ladder | MATHEMATICS | 3-SPHERE | Mobius ladder | SPATIAL GRAPHS | COMPLETE GRAPHS | Classification | Group theory | Graphs | Knot theory | Topology | Orientation | Ladders | Preserving | Symmetry
Journal Article
Symmetry (Basel), ISSN 2073-8994, 2014, Volume 6, Issue 2, pp. 189 - 209
Topological symmetry groups were originally introduced to study the symmetries of non-rigid molecules, but have since been used to study the symmetries of any... 
Complete graphs | Spatial graphs | Molecular symmetries | Topological symmetry groups | spatial graphs | MULTIDISCIPLINARY SCIENCES | PERIOD | 3-SPHERE | molecular symmetries | topological symmetry groups | KNOTS | complete graphs | Graphs | Topology | Orientation | Preserving | Group theory | Symmetry
Journal Article
Tokyo Journal of Mathematics, ISSN 0387-3870, 06/2014, Volume 37, Issue 1, pp. 135 - 158
We determine for which n, the complete bipartite graph K-n,K-n has an embedding in S-3 whose topological symmetry group is isomorphic to one of the polyhedral... 
Spatial graphs | Topological symmetry groups | MATHEMATICS | 3-SPHERE | spatial graphs | 05C10 | 57M25
Journal Article
数学年刊:B辑英文版, ISSN 0252-9599, 2015, Volume 36, Issue 2, pp. 161 - 180
Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S^3.... 
嵌入 | 作者 | 地图 | 副产品 | 映射 | 对称性 | 周期性 | 曲面 | 57M60 | 57S25 | 57S17 | Mathematics, general | Mathematics | Extendable action | Applications of Mathematics | Symmetry of surface | Symmetry of 3-sphere | MATHEMATICS
Journal Article
Algebraic & geometric topology, ISSN 1472-2739, 2011, Volume 11, Issue 3, pp. 1405 - 1433
We determine for which m the complete graph K-m has an embedding in S-3 whose topological symmetry group is isomorphic to one of the polyhedral groups A(4),... 
MATHEMATICS | 3-SPHERE
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 09/1995, Volume 4, Issue 3, pp. 373 - 388
In this paper we show that, for any 3-connected graph G, if an automorphism of G is realizable by a homeomorphism of (S3, G) then there is an embedding of G... 
MATHEMATICS | SYMMETRIES OF GRAPHS | EMBEDDED GRAPHS | CHIRALITY
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 08/1998, Volume 7, Issue 5, pp. 651 - 657
In this paper, a new equivalence relation, weak isotopy, on spatial graphs will be introduced. By using a rearrangement theorem (Theorem 1), it is shown that,... 
Embedded graphs | Weak isotopy | Minimum embeddings | Topological symmetry groups | MATHEMATICS | 3-MANIFOLDS | weak isotopy | minimum embeddings | embedded graphs | topological symmetry groups
Journal Article
Revista matemática complutense, ISSN 1988-2807, 2011, Volume 25, Issue 2, pp. 493 - 510
It is shown that for any locally knotted edge of a 3-connected graph in S 3, there is a ball that contains all of the local knots of that edge which is unique... 
05C10 | Prime decomposition | Mathematics | 57M15 | Topology | 57M25 | Local knots | Topological symmetry groups | Geometry | Algebra | Analysis | Spatial graphs | Mathematics, general | Applications of Mathematics | Prime Decomposition | MATHEMATICS | MATHEMATICS, APPLIED | 3-SPHERE | Mathematics - Geometric Topology
Journal Article
Physics Letters B, ISSN 0370-2693, 11/2005, Volume 628, Issue 1-2, pp. 33 - 39
A possibility of the crystalline state of nuclear matter is discussed in a medium-modified Skyrme model. The interaction energy per nucleon in nuclear matter... 
Skyrme model | Medium modifications | Nuclear matter | Crystalline structure | SYMMETRY | nuclear matter | PHYSICS, MULTIDISCIPLINARY | 3-SPHERE | MODEL | crystalline structure | medium modifications | DENSE SKYRMION MATTER | Structure | Analysis | Radiation | Crystals
Journal Article
FUNDAMENTA MATHEMATICAE, ISSN 0016-2736, 2014, Volume 226, Issue 1, pp. 1 - 16
We characterize which automorphisms of an arbitrary complete bipartite graph K-n,K-m can be induced by a homeomorphism of some embedding of the graph in S-3. 
MATHEMATICS | spatial graphs | bipartite graphs | 3-SPHERE | topological symmetry groups
Journal Article
TOPOLOGY AND ITS APPLICATIONS, ISSN 0166-8641, 10/2013, Volume 160, Issue 16, pp. 2088 - 2103
.... Efforts are made to see intuitively how these maximal symmetries are embedded into the symmetries of the 3-sphere. (C) 2013 Elsevier B.V... 
MATHEMATICS | MATHEMATICS, APPLIED | Maximum order | NUMBER | Extendable action | AUTOMORPHISMS | Symmetry of surface | Symmetry of 3-sphere | Finite group action
Journal Article
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