Punctured torus groups and 2-bridge knot groups

Punctured torus groups and 2-bridge knot groups PDF Author: Hirotaka Akiyoshi
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Punctured torus groups and 2-bridge knot groups

Punctured torus groups and 2-bridge knot groups PDF Author: Hirotaka Akiyoshi
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description


Punctured Torus Groups and 2-Bridge Knot Groups (I)

Punctured Torus Groups and 2-Bridge Knot Groups (I) PDF Author: Hirotaka Akiyoshi
Publisher: Springer
ISBN: 3540718079
Category : Mathematics
Languages : en
Pages : 293

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Book Description
Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.

Punctured Torus Groups and 2-Bridge Knot Groups (I)

Punctured Torus Groups and 2-Bridge Knot Groups (I) PDF Author: Hirotaka Akiyoshi
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 308

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Book Description
Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.

Characters in Low-Dimensional Topology

Characters in Low-Dimensional Topology PDF Author: Olivier Collin
Publisher: American Mathematical Soc.
ISBN: 147045209X
Category : Education
Languages : en
Pages : 372

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Book Description
This volume contains the proceedings of a conference celebrating the work of Steven Boyer, held from June 2–6, 2018, at Université du Québec à Montréal, Montréal, Québec, Canada. Boyer's contributions to research in low-dimensional geometry and topology, and to the Canadian mathematical community, were recognized during the conference. The articles cover a broad range of topics related, but not limited, to the topology and geometry of 3-manifolds, properties of their fundamental groups and associated representation varieties.

Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds

Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds PDF Author: Rainer Weissauer
Publisher: Springer
ISBN: 3540893067
Category : Mathematics
Languages : en
Pages : 384

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Book Description
This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder [40] and Laumon [62]. In writing this text based on a revised version of these preprints that were widely distributed in summer 1995, I ?nally did not p- sue the original plan to completely reorganize the original preprints. After the long delay, one of the reasons was that an overview of the results is now available in [115]. Instead I tried to improve the presentation modestly, in particular by adding cross-references wherever I felt this was necessary. In addition, Chaps. 11 and 12 and Sects. 5. 1, 5. 4, and 5. 5 were added; these were written in 1998. I willgivea moredetailedoverviewofthecontentofthedifferentchaptersbelow. Before that I should mention that the two main results are the proof of Ramanujan’s conjecture for Siegel modular forms of genus 2 for forms which are not cuspidal representations associated with parabolic subgroups(CAP representations), and the study of the endoscopic lift for the group GSp(4). Both topics are formulated and proved in the ?rst ?ve chapters assuming the stabilization of the trace formula. All the remaining technical results, which are necessary to obtain the stabilized trace formula, are presented in the remaining chapters. Chapter 1 gathers results on the cohomology of Siegel modular threefolds that are used in later chapters, notably in Chap. 3. At the beginning of Chap.

Random Polymers

Random Polymers PDF Author: Frank den Hollander
Publisher: Springer
ISBN: 3642003338
Category : Mathematics
Languages : en
Pages : 271

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Book Description
Polymer chains that interact with themselves and/or with their environment are fascinating objects, displaying a range of interesting physical and chemical phenomena. The focus in this monograph is on the mathematical description of some of these phenomena, with particular emphasis on phase transitions as a function of interaction parameters, associated critical behavior and space-time scaling. Topics include: self-repellent polymers, self-attracting polymers, polymers interacting with interfaces, charged polymers, copolymers near linear or random selective interfaces, polymers interacting with random substrate and directed polymers in random environment. Different techniques are exposed, including the method of local times, large deviations, the lace expansion, generating functions, the method of excursions, ergodic theory, partial annealing estimates, coarse-graining techniques and martingales. Thus, this monograph offers a mathematical panorama of polymer chains, which even today holds plenty of challenges.

Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems

Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems PDF Author: Torsten Linß
Publisher: Springer
ISBN: 3642051340
Category : Mathematics
Languages : en
Pages : 331

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Book Description
This is a book on numerical methods for singular perturbation problems – in part- ular, stationary reaction-convection-diffusion problems exhibiting layer behaviour. More precisely, it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. Numerical methods for singularly perturbed differential equations have been studied since the early 1970s and the research frontier has been constantly - panding since. A comprehensive exposition of the state of the art in the analysis of numerical methods for singular perturbation problems is [141] which was p- lished in 2008. As that monograph covers a big variety of numerical methods, it only contains a rather short introduction to layer-adapted meshes, while the present book is exclusively dedicated to that subject. An early important contribution towards the optimisation of numerical methods by means of special meshes was made by N.S. Bakhvalov [18] in 1969. His paper spawned a lively discussion in the literature with a number of further meshes - ing proposed and applied to various singular perturbation problems. However, in the mid 1980s, this development stalled, but was enlivened again by G.I. Shishkin’s proposal of piecewise-equidistant meshes in the early 1990s [121,150]. Because of their very simple structure, they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on c- peting meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue.

Séminaire de Probabilités XLII

Séminaire de Probabilités XLII PDF Author: Catherine Donati-Martin
Publisher: Springer
ISBN: 3642017630
Category : Mathematics
Languages : en
Pages : 457

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Book Description
This book offers an introduction to rough paths. Coverage also includes the interface between analysis and probability to special processes, Lévy processes and Lévy systems, representation of Gaussian processes, filtrations and quantum probability.

Mathematical Modeling in Biomedical Imaging I

Mathematical Modeling in Biomedical Imaging I PDF Author: Habib Ammari
Publisher: Springer
ISBN: 3642034446
Category : Mathematics
Languages : en
Pages : 244

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Book Description
This volume details promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.

Potential Analysis of Stable Processes and its Extensions

Potential Analysis of Stable Processes and its Extensions PDF Author: Krzysztof Bogdan
Publisher: Springer Science & Business Media
ISBN: 3642021417
Category : Mathematics
Languages : en
Pages : 200

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Book Description
Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schrödinger operators. The authors focus on classes of stable and related processes that contain the Brownian motion as a special case. This is the first book devoted to the probabilistic potential theory of stable stochastic processes, and, from the analytical point of view, of the fractional Laplacian. The introduction is accessible to non-specialists and provides a general presentation of the fundamental objects of the theory. Besides recent and deep scientific results the book also provides a didactic approach to its topic, as all chapters have been tested on a wide audience, including young mathematicians at a CNRS/HARP Workshop, Angers 2006. The reader will gain insight into the modern theory of stable and related processes and their potential analysis with a theoretical motivation for the study of their fine properties.