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Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 03/2007, Volume 142, Issue 2, pp. 269 - 287
The famous Haken–Kneser–Milnor theorem states that every 3-manifold can be expressed in a unique way as a connected sum of prime 3-manifolds. The analogous... 
MATHEMATICS | Theorems | Mathematics | Mathematics - Geometric Topology
Journal Article
Nonlinearity, ISSN 1361-6544, 2017, Volume 30, Issue 11, pp. 3993 - 4028
This paper initiates the study of semitoric integrable systems with two degrees of freedom and with proper momentum-energy map, but with possibly nonproper... 
57M60 | 57S25 | 57R17 | 58D27 | 53D20 | 70H06 | integrable Mathematics Subject Classification numbers: 37J35 | semitoric | sympletic | TOPOLOGY | MATHEMATICS, APPLIED | CONVEXITY | SINGULARITIES | HAMILTONIAN-SYSTEMS | integrable | NORMAL FORMS | PHYSICS, MATHEMATICAL
Journal Article
Czechoslovak Mathematical Journal, ISSN 0011-4642, 12/2011, Volume 61, Issue 4, pp. 1037 - 1047
We prove that if the Walsh bipartite map M = W (ℋ) of a regular oriented hypermap ℋ is also orientably regular then both M and ℋ have the same chirality group,... 
toroidal hypermaps | 05C10 | 57M60 | 51E30 | regular covering | Mathematics | chirality group | 20B25 | 20F65 | Ordinary Differential Equations | chirality index | Convex and Discrete Geometry | Analysis | 57M07 | Mathematics, general | Mathematical Modeling and Industrial Mathematics | 05C25 | hypermap | MATHEMATICS | MAPS
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 2010, Volume 10, Issue 3, pp. 1609 - 1625
Let epsilon denote the group of all interval exchange transformations on [0, 1). Given a suitable topological group structure on epsilon, it is possible to... 
DIFFEOMORPHISMS | MATHEMATICS | TRANSFORMATIONS | GROWTH | Mathematics - Dynamical Systems
Journal Article
The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2007, Volume 37, Issue 4, pp. 1251 - 1269
Let G be a finite group. The real genus ρ(G) is the minimum algebraic genus of any compact bordered Klein surface on which G acts. Here we consider groups of... 
Integers | Homomorphisms | Algebra | Mathematical theorems | Quotients | Mathematical surfaces | Signatures | Automorphisms | MATHEMATICS | AUTOMORPHISMS | BOUNDARY | KLEIN SURFACES | BORDERED SURFACES | 57M60 | 30F50 | 20H10
Journal Article
The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2010, Volume 40, Issue 5, pp. 1527 - 1578
It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms.... 
Equivalence relation | Natural order | Mathematical sequences | Mathematical theorems | Logical theorems | Homeomorphism | Partially ordered sets | Mathematics | Real lines | Convexity | Order tree | 3-manifold | Tree | Group action | 1-manifold | Partially ordered group | 20F65 | 57M60 | 20F60 | tree | 20E08 | 06F15 | group action | order tree
Journal Article
Revista Matemática Complutense, ISSN 1139-1138, 1/2012, Volume 25, Issue 1, pp. 221 - 245
We consider (n,q)-gonal Klein surfaces of algebraic genus p≥2 for which n≥p and n prime. We exclude the case n=2 corresponding to q-hyperelliptic surfaces, so... 
57M60 | 30F50 | Klein surfaces | Mathematics | Topology | Automorphisms | Fundamental regions | NEC groups | Geometry | Algebra | Hyperbolic polygons | Analysis | Mathematics, general | 20F05 | Applications of Mathematics | 20H10 | MATHEMATICS | MATHEMATICS, APPLIED | RIEMANN SURFACES | TEICHMULLER SPACE
Journal Article
Experimental Mathematics, ISSN 1058-6458, 01/2007, Volume 16, Issue 2, pp. 167 - 179
The minimum dilatation of pseudo-Anosov 5-braids is shown to be the largest zero λ 5 ≈ 1.72208 of x 4 -x 3 -x 2 -x+1, which is attained by σ 1 σ 2 σ 3 σ 4 σ 1... 
Dilation | Secondary 37B40, 57M60 | Primary 37E30 | train track | braid | Braid | Train track | DIFFEOMORPHISMS | BRAIDS | AUTOMORPHISMS | TRAIN-TRACKS | MATHEMATICS | dilation | HOMEOMORPHISMS | LOWER BOUNDS | MAPS | DISK | ENTROPY | SURFACES
Journal Article
Michigan Mathematical Journal, ISSN 0026-2285, 1999, Volume 46, Issue 2, pp. 281 - 296
Journal Article
Homology, Homotopy and Applications, ISSN 1532-0073, 2008, Volume 10, Issue 2, pp. 139 - 148
We study a correspondence between orientation-reversing involutions on compact 3-manifolds with only isolated fixed points and self-dual, binary codes. We show... 
3-manifold | Involution | Cohomology | Code | MATHEMATICS | MATHEMATICS, APPLIED | code | involution | cohomology | 57M60 | 57M50 | 94B05 | 57R91
Journal Article
Topology and its Applications, ISSN 0166-8641, 2008, Volume 155, Issue 9, pp. 946 - 964
Let G be a cyclic group of order 3, 5 or 7, and X = E ( n ) be the relatively minimal elliptic surface with rational base. In this paper, we prove that under... 
Elliptic surface | Locally linear | Seiberg–Witten invariants | Group actions | Seiberg-Witten invariants | MATHEMATICS | MATHEMATICS, APPLIED | elliptic surface | SMOOTH GROUP-ACTIONS | COMPLEXES | 4-MANIFOLDS | FIXED POINT FORMULA | group actions | locally linear
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 01/2006, Volume 252, Issue 1, pp. 19 - 25
We prove that closed symplectic four-manifolds do not admit any smooth free circle actions with contractible orbits, without assuming that the actions preserve... 
57M60 | Mathematics, general | Mathematics | 57R17 | 57R91 | 57R57 | MATHEMATICS | 4-MANIFOLDS | INVARIANTS
Journal Article
Journal of Homotopy and Related Structures, ISSN 2193-8407, 12/2019, Volume 14, Issue 4, pp. 919 - 992
We use equivariant surgery to classify all involutions on closed surfaces, up to isomorphism. Work on this problem is classical, dating back to the nineteenth... 
57M60 | Involution | Algebra | Functional Analysis | Algebraic Topology | Surgery | Mathematics | Number Theory | Equivariant | 55M35 | Surface | MATHEMATICS | CLASSIFICATION
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 6/2005, Volume 2, Issue 2, pp. 215 - 229
We prove that given a $$\mathcal{C}^\infty $$ Riemannian manifold with boundary, having a finite number of compact boundary components, any fat triangulation... 
30C65 | Primary 57R05 | Fat triangulation | Secondary 57M60 | Mathematics, general | Mathematics | quasimeromorphic mapping | Quasimeromorphic mapping | MATHEMATICS | MATHEMATICS, APPLIED | fat triangulation
Journal Article
The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2009, Volume 39, Issue 2, pp. 381 - 398
We study the topology and geometry of some series of closed connected orientable 3-manifolds constructed as honey-comb spaces. These manifolds are quotients of... 
Mathematical manifolds | Geometry | Series convergence | Mathematical theorems | Homeomorphism | Mathematics | Cognitive space | Symmetry | Vertices | Topological spaces | Branched coverings | Polyhedral schemata | Three-manifolds | Orbifolds | Spines | Group presentations | MATHEMATICS | branched coverings | spines | group presentations | orbifolds | polyhedral schemata | 57M60 | 57M50 | 57M12 | 57M25
Journal Article
Michigan Mathematical Journal, ISSN 0026-2285, 1998, Volume 45, Issue 2, pp. 315 - 332
Journal Article
Communications in Algebra, ISSN 0092-7872, 11/2017, Volume 45, Issue 11, pp. 4730 - 4739
Let G be a finite group. The strong symmetric genus σ 0 (G) is the minimum genus of any Riemann surface on which G acts faithfully and preserving orientation.... 
Primary: 20F38 | Secondary: 20D15, 20H10, 30F50, 57M60 | strong symmetric genus | Density | Riemann surface | p-group | MATHEMATICS | CONTAIN | ORDER P(M) | SURFACES | Integers | Group theory
Journal Article
The Asian journal of mathematics, ISSN 1093-6106, 2006, Volume 10, Issue 4, pp. 731 - 748
We give an alternative proof of the mod p vanishing theorem by F. Fang of Seiberg-Witten invariants under a cyclic group action of prime order, and generalize... 
57M60 | 57S17 | 4-manifolds | Seiberg-Witten invariants | 57R57 | group actions
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 2/2006, Volume 117, Issue 1, pp. 161 - 180
Real-analytic actions of SL(2;R) on surfaces have been classified, up to analytic change of coordinates. In particular it is known that there exists countably... 
Geometry | Mathematics | 57M60 (53C35) | SL(2, R) | hyperbolic plane | differentiable compactification | SL(2,R) | Hyperbolic plane | Differentiable compactification | MATHEMATICS
Journal Article
The Rocky Mountain journal of mathematics, ISSN 0035-7596, 10/2009, Volume 39, Issue 5, pp. 1573 - 1595
Journal Article
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