scholarly journals On hyperbolic surface bundles over the circle as branched double covers of the $3$-sphere

2020 ◽  
Vol 148 (4) ◽  
pp. 1805-1814
Author(s):  
Susumu Hirose ◽  
Eiko Kin
Keyword(s):  
Hyperbolic Surface ◽  
Double Covers ◽  
Surface Bundles

scholarly journals Pseudo-Anosov extensions and degree one maps between hyperbolic surface bundles

2007 ◽  
Vol 256 (4) ◽  
pp. 913-923 ◽  
Author(s):  
Michel Boileau ◽  
Yi Ni ◽  
Shicheng Wang
Keyword(s):  
Hyperbolic Surface ◽  
Surface Bundles

scholarly journals Erratum to: Pseudo-Anosov extensions and degree one maps between hyperbolic surface bundles

2015 ◽  
Vol 279 (3-4) ◽  
pp. 1225-1226
Author(s):  
Michel Boileau ◽  
Yi Ni ◽  
Shicheng Wang
Keyword(s):  
Hyperbolic Surface ◽  
Surface Bundles

Arithmetic hyperbolic surface bundles

1995 ◽  
Vol 302 (1) ◽  
pp. 31-60 ◽  
Author(s):  
B. H. Bowditch ◽  
C. Maclachlan ◽  
A. W. Reid
Keyword(s):  
Hyperbolic Surface ◽  
Surface Bundles

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

scholarly journals A Dynamic Hyperbolic Surface Model for Responsive Data Mining

2021 ◽  
Vol 185 ◽  
pp. 170-176
Author(s):  
W. Glenn Bond ◽  
Maria A. Seale ◽  
Jeffrey L. Hensley
Keyword(s):  
Data Mining ◽  
Hyperbolic Surface ◽  
Surface Model

scholarly journals EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES

2020 ◽  
pp. 1-36
Author(s):  
Bart Michels
Keyword(s):  
Lower Bound ◽  
Closed Geodesic ◽  
Extreme Values ◽  
Theta Series ◽  
Hyperbolic Surface ◽  
Quadratic Fields ◽  
Maass Forms ◽  
Real Quadratic Fields ◽  
Central Values ◽  
Real Quadratic

Abstract Given a closed geodesic on a compact arithmetic hyperbolic surface, we show the existence of a sequence of Laplacian eigenfunctions whose integrals along the geodesic exhibit nontrivial growth. Via Waldspurger’s formula we deduce a lower bound for central values of Rankin-Selberg L-functions of Maass forms times theta series associated to real quadratic fields.

Double cover K3 surfaces of Hirzebruch surfaces

2021 ◽  
Vol 21 (2) ◽  
pp. 221-225
Author(s):  
Taro Hayashi
Keyword(s):  
Rational Surface ◽  
K3 Surfaces ◽  
Double Cover ◽  
Double Covering ◽  
Smooth Surfaces ◽  
Branch Locus ◽  
Hirzebruch Surfaces ◽  
Double Covers

Abstract General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.

scholarly journals Varieties of minimal rational tangents on double covers of projective space

2012 ◽  
Vol 275 (1-2) ◽  
pp. 109-125 ◽  
Author(s):  
Jun-Muk Hwang ◽  
Hosung Kim
Keyword(s):  
Projective Space ◽  
Double Covers

Small Cycle Double Covers of Products II: Categorical and Strong Products with Paths and Cycles

2009 ◽  
Vol 25 (3) ◽  
pp. 385-400 ◽  
Author(s):  
R. J. Nowakowski ◽  
K. Seyffarth
Keyword(s):  
Small Cycle ◽  
Double Covers
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