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Inventiones mathematicae, ISSN 0020-9910, 3/2019, Volume 215, Issue 3, pp. 819 - 862
We extend the notion of canonical measures to all (possibly non-compact) metric graphs. This will allow us to introduce a notion of “hyperbolic measures” on... 
20F65 | 57M60 | 05C12 | 05C63 | Mathematics, general | 14H30 | Mathematics | 14T05 | Graphs | Theorems | Riemann surfaces | Constraining
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 12/2019, Volume 100, Issue 3, pp. 851 - 870
Earlier work introduced a geometrically natural probability measure on the group of all Möbius transformations of the hyperbolic plane so as to be able to... 
30F40 | 30C60 | 53A35 | 30D50 | 22E40 | 57N13 | 20H10 | 57M60 (primary)
Journal Article
Michigan Mathematical Journal, ISSN 0026-2285, 11/2017, Volume 66, Issue 4, pp. 885 - 890
We characterize the cyclic branched covers of the 2-sphere where every homeomorphism of the sphere lifts to a homeomorphism of the covering surface. This... 
MATHEMATICS | SURFACES | Mathematics - Geometric Topology
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 08/2017, Volume 49, Issue 4, pp. 604 - 629
We study the Birman exact sequence for compact 3‐manifolds, obtaining a complete picture of the relationship between the mapping class group of the manifold... 
57M05, 57M10 (secondary) | 57M60 (primary) | MATHEMATICS | Mathematics - Geometric Topology
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2012, Volume 161, Issue 9, pp. 1613 - 1656
We present a structure theorem for the subsurface projections of train-track splitting sequences. For the proof we introduce induced tracks, efficient... 
MATHEMATICS | COMPLEX | CURVES | GEOMETRY | Mathematics - Geometric Topology | 57M60 | 20F65
Journal Article
Journal of Topology, ISSN 1753-8416, 06/2018, Volume 11, Issue 2, pp. 283 - 308
As a consequence of a general result about finite group actions on 3‐manifolds, we show that a hyperbolic 3‐manifold can be the cyclic branched cover of at... 
57M60 | 57M12 | 57M40 | 57S17 (primary) | 57M25 | 57M50 (secondary) | MATHEMATICS | LINKS | 3-SPHERES | HYPERBOLIC KNOTS | SPACES
Journal Article
Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 10/2014, Volume 20, Issue 2, pp. 611 - 621
A finite nonabelian simple group does not admit a free action on a homology sphere, and the only finite simple group which acts on a homology sphere with at... 
57M60 | 57S25 | Mathematics, general | 57S17 | Mathematics | MATHEMATICS
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 10/2018, Volume 98, Issue 2, pp. 253 - 274
Marked Schottky space MSg is an explicit model of the quasiconformal deformation space of a Schottky group of rank g, this being isomorphic to the punctured... 
57M50 | 30F60 | 57M60 (secondary) | 32G15 | 30F10 | 30F40 (primary) | 57M10 | FORMS | MATHEMATICS | ABELIAN-VARIETIES | GENERATED KLEINIAN GROUPS | ALGEBRAIC-CURVES | MODULI SPACES | TEICHMULLER-SPACES | Mathematics - Complex Variables
Journal Article
Tohoku Mathematical Journal, Second Series, ISSN 0040-8735, 2010, Volume 62, Issue 1, pp. 45 - 53
Kulkarni showed that, if $g$ is greater than three, any periodic map on the oriented surface of genus $g$ with period more than or equal to $4g$ is conjugate... 
MATHEMATICS | AUTOMORPHISMS
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 2/2017, Volume 186, Issue 1, pp. 39 - 74
Let $$\mathcal {X}_S$$ X S denote the class of spaces homeomorphic to two closed orientable surfaces of genus greater than one identified to each other along... 
Geometry | 57M60 | 57M07 | Amalgamated products | 20E07 | Mathematics | Abstract commensurability | Surface groups | Quasi-isometry classification | MATHEMATICS | COVERINGS | MANIFOLDS
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 3/2018, Volume 59, Issue 2, pp. 331 - 362
We consider the orientation-preserving actions of finite groups G on pairs $$(S^3, \Gamma )$$ (S3,Γ) , where $$\Gamma $$ Γ is a connected graph of genus... 
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
Bulletin of the London Mathematical Society, ISSN 0024-6093, 06/2018, Volume 50, Issue 3, pp. 390 - 394
In the Cayley graph of the mapping class group of a closed surface, with respect to any generating set, we look at a ball of large radius centered on the... 
20F65 | 57M60 | 20P05 (secondary) | 57S30 (primary) | 57M07 | MATHEMATICS | Group Theory | Geometric Topology | Mathematics
Journal Article
数学学报:英文版, ISSN 1439-8516, 2016, Volume 32, Issue 1, pp. 54 - 68
We determine the maximum order Eg of finite groups G acting on the closed surface E9 of genus g which extends over (S3, ∑g) for all possible embeddings ∑g →... 
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
Communications in Mathematical Physics, ISSN 0010-3616, 12/2017, Volume 356, Issue 2, pp. 427 - 449
The notion of fractional monodromy was introduced by Nekhoroshev, Sadovskií and Zhilinskií as a generalization of standard (‘integer’) monodromy in the sense... 
NEIGHBORHOODS | POINTS | FOCUS-FOCUS | INTEGRABLE HAMILTONIAN-SYSTEMS | To be checked by Faculty | CYCLES | Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHYSICS, MATHEMATICAL | Computer science
Journal Article
Michigan Mathematical Journal, ISSN 0026-2285, 11/2011, Volume 60, Issue 3, pp. 483 - 493
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 01/2015, Volume 291, pp. 62 - 73
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality... 
Dimensionality reduction | Collective behavior | Algorithm | Dynamical systems | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | DYNAMICS | PHYSICS, MATHEMATICAL | ISOMAP
Journal Article
Nagoya Mathematical Journal, ISSN 0027-7630, 2013, Volume 210, pp. 83 - 132
We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric... 
MATHEMATICS | Mathematics - Algebraic Geometry | 57M60 | 14P25 | 20F36 | 11F06
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 8/2014, Volume 103, Issue 2, pp. 195 - 200
By a classical result of Jordan, each finite subgroup of a complex linear group $${{\rm GL}_n(\mathbb{C})}$$ GL n ( C ) has an abelian normal subgroup whose... 
57M60 | 3-manifold | Mathematics, general | Mathematics | Jordan bound | Finite group action | MATHEMATICS | MANIFOLDS | THEOREM
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 4/2017, Volume 108, Issue 4, pp. 341 - 350
Let $${\mathcal {S}}$$ S denote the set of positive integers that may appear as the strong symmetric genus of a finite abelian group. We obtain a set of... 
Primary 57M60 | Mathematics | 30F99 | Unions of arithmetic progressions | Secondary 11B05 | Riemann surface | 11N25 | Abelian groups | Mathematics, general | 20F38 | 11N37 | Strong symmetric genus | Genus spectrum | Asymptotic density | MATHEMATICS
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2018, Volume 288, Issue 3, pp. 829 - 853
We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the... 
57M60 | 57S25 | Cohomogeneity one | Group action | Smoothing | 57S10 | 57N15 | Mathematics, general | Topological manifold | Mathematics | 57R10 | LOW DIMENSIONS | SPACES | SPHERES | CLASSIFICATION | FORMULA | MATHEMATICS | INDEX | POSITIVE RICCI CURVATURE | GEOMETRY | Algebra
Journal Article
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