Braids Links And Mapping Class Groups Am 82 Volume 82
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Braids Conformal Module Entropy And Gromov S Oka Principle
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Author : Burglind Jöricke
language : en
Publisher: Springer Nature
Release Date : 2025-01-31
Braids Conformal Module Entropy And Gromov S Oka Principle written by Burglind Jöricke and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-31 with Mathematics categories.
This book studies the relation between conformal invariants and dynamical invariants and their applications, taking the reader on an excursion through a wide range of topics. The conformal invariants, called here the conformal modules of conjugacy classes of elements of the fundamental group, were proposed by Gromov in the case of the twice punctured complex plane. They provide obstructions to Gromov's Oka Principle. The invariants of the space of monic polynomials of degree n appeared earlier in relation to Hilbert's 13th Problem, and are called the conformal modules of conjugacy classes of braids. Interestingly, the conformal module of a conjugacy class of braids is inversely proportional to a popular dynamical invariant, the entropy, which was studied in connection with Thurston's celebrated theory of surface homeomorphisms. This result, proved here for the first time, is another instance of the numerous manifestations of the unity of mathematics, and it has applications. After prerequisites on Riemann surfaces, braids, mapping classes and elements of Teichmüller theory, a detailed introduction to the entropy of braids and mapping classes is given, with thorough, sometimes new proofs. Estimates are provided of Gromov's conformal invariants of the twice punctured complex plane and it is shown that the upper and lower bounds differ by universal multiplicative constants. These imply estimates of the entropy of any pure three-braid, and yield quantitative statements on the limitations of Gromov's Oka Principle in the sense of finiteness theorems, using conformal invariants which are related to elements of the fundamental group (not merely to conjugacy classes). Further applications of the concept of conformal module are discussed. Aimed at graduate students and researchers, the book proposes several research problems.
The Lower Algebraic K Theory Of Virtually Cyclic Subgroups Of The Braid Groups Of The Sphere And Of Zb4 S2
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Author : John Guaschi
language : en
Publisher: Springer
Release Date : 2018-11-03
The Lower Algebraic K Theory Of Virtually Cyclic Subgroups Of The Braid Groups Of The Sphere And Of Zb4 S2 written by John Guaschi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.
This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools. Many of the techniques extend to the general case, and the results reveal new K-theoretical phenomena with respect to the previous study of other families of groups. The second part of the manuscript focusses on the case of the 4-string braid group of the 2-sphere, which is shown to be hyperbolic in the sense of Gromov. This permits the computation of the infinite maximal virtually cyclic subgroups of this group and their conjugacy classes, and applying the fact that this group satisfies the Fibred Isomorphism Conjecture of Farrell and Jones, leads to an explicit calculation of its lower K-theory. Researchers and graduate students working in K-theory and surface braid groups will constitute the primary audience of the manuscript, particularly those interested in the Fibred Isomorphism Conjecture, and the computation of Nil groups and the lower algebraic K-groups of group rings. The manuscript will also provide a useful resource to researchers who wish to learn the techniques needed to calculate lower algebraic K-groups, and the bibliography brings together a large number of references in this respect.
Braids And Dynamics
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Author : Jean-Luc Thiffeault
language : en
Publisher: Springer Nature
Release Date : 2022-09-05
Braids And Dynamics written by Jean-Luc Thiffeault and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-05 with Mathematics categories.
This monograph uses braids to explore dynamics on surfaces, with an eye towards applications to mixing in fluids. The text uses the particular example of taffy pulling devices to represent pseudo-Anosov maps in practice. In addition, its final chapters also briefly discuss current applications in the emerging field of analyzing braids created from trajectory data. While written with beginning graduate students, advanced undergraduates, or practicing applied mathematicians in mind, the book is also suitable for pure mathematicians seeking real-world examples. Readers can benefit from some knowledge of homotopy and homology groups, but these concepts are briefly reviewed. Some familiarity with Matlab is also helpful for the computational examples.
Perspectives In Lie Theory
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Author : Filippo Callegaro
language : en
Publisher: Springer
Release Date : 2017-12-07
Perspectives In Lie Theory written by Filippo Callegaro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-07 with Mathematics categories.
Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.
Knots And Primes
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Author : Masanori Morishita
language : en
Publisher: Springer Nature
Release Date : 2024-05-27
Knots And Primes written by Masanori Morishita and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-27 with Mathematics categories.
This book provides a foundation for arithmetic topology, a new branch of mathematics that investigates the analogies between the topology of knots, 3-manifolds, and the arithmetic of number fields. Arithmetic topology is now becoming a powerful guiding principle and driving force to obtain parallel results and new insights between 3-dimensional geometry and number theory. After an informative introduction to Gauss' work, in which arithmetic topology originated, the text reviews a background from both topology and number theory. The analogy between knots in 3-manifolds and primes in number rings, the founding principle of the subject, is based on the étale topological interpretation of primes and number rings. On the basis of this principle, the text explores systematically intimate analogies and parallel results of various concepts and theories between 3-dimensional topology and number theory. The presentation of these analogies begins at an elementary level, gradually building to advanced theories in later chapters. Many results presented here are new and original. References are clearly provided if necessary, and many examples and illustrations are included. Some useful problems are also given for future research. All these components make the book useful for graduate students and researchers in number theory, low dimensional topology, and geometry. This second edition is a corrected and enlarged version of the original one. Misprints and mistakes in the first edition are corrected, references are updated, and some expositions are improved. Because of the remarkable developments in arithmetic topology after the publication of the first edition, the present edition includes two new chapters. One is concerned with idelic class field theory for 3-manifolds and number fields. The other deals with topological and arithmetic Dijkgraaf–Witten theory, which supports a new bridge between arithmetic topology and mathematical physics.
Surface Knots In 4 Space
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Author : Seiichi Kamada
language : en
Publisher: Springer
Release Date : 2017-03-28
Surface Knots In 4 Space written by Seiichi Kamada and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-28 with Mathematics categories.
This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.Knot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval.Included in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surface diagrams, handle surgeries, ribbon surface-knots, spinning construction, knot concordance and 4-genus, quandles and their homology theory, and two-dimensional braids.
Public Key Cryptography Pkc 2019
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Author : Dongdai Lin
language : en
Publisher: Springer
Release Date : 2019-04-08
Public Key Cryptography Pkc 2019 written by Dongdai Lin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-08 with Computers categories.
The two-volume set LNCS 11442 and 11443 constitutes the refereed proceedings of the 22nd IACR International Conference on the Practice and Theory of Public-Key Cryptography, PKC 2019, held in Beijing, China, in April 2019. The 42 revised papers presented were carefully reviewed and selected from 173 submissions. They are organized in topical sections such as: Cryptographic Protocols; Digital Signatures; Zero-Knowledge; Identity-Based Encryption; Fundamental Primitives; Public Key Encryptions; Functional Encryption; Obfuscation Based Cryptography; Re- Encryption Schemes; Post Quantum Cryptography.
Knot Theory
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Author : Charles Livingston
language : en
Publisher: Cambridge University Press
Release Date : 1993
Knot Theory written by Charles Livingston and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This book uses only linear algebra and basic group theory to study the properties of knots.
Mapping Class Groups And Moduli Spaces Of Riemann Surfaces
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Author : Carl-Friedrich Bödigheimer
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Mapping Class Groups And Moduli Spaces Of Riemann Surfaces written by Carl-Friedrich Bödigheimer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The study of mapping class groups and moduli spaces of compact Riemann surfaces is currently a central topic in topology, algebraic geometry, and conformal field theory. This book contains proceedings from two workshops held in the summer of 1991, one at the University of G\"ottingen and the other at the University of Washington at Seattle. The papers gathered here represent diverse approaches and contain several important new results. With both research and survey articles, the book appeals to mathematicians and physicists.
Knots Low Dimensional Topology And Applications
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Author : Colin C. Adams
language : en
Publisher: Springer
Release Date : 2019-06-26
Knots Low Dimensional Topology And Applications written by Colin C. Adams and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-26 with Mathematics categories.
This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.