Download or read book Monoidal Topology written by Dirk Hofmann and published by Cambridge University Press. This book was released on 2014-07-31 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lax-algebraic and categorical methods, Monoidal Topology provides a unified theory for metric and topological structures with far-reaching applications.
Download or read book Monoidal Categories and Topological Field Theory written by Vladimir Turaev and published by Birkhäuser. This book was released on 2017-06-28 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category. The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.
Download or read book Topological Groups and Related Structures An Introduction to Topological Algebra written by Alexander Arhangel’skii and published by Springer Science & Business Media. This book was released on 2008-05-01 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.
Download or read book Topological Duality for Distributive Lattices written by Mai Gehrke and published by Cambridge University Press. This book was released on 2024-02-29 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing Stone-Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.
Download or read book Index Analysis written by R. Lowen and published by Springer. This book was released on 2015-01-06 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: The featured review of the AMS describes the author’s earlier work in the field of approach spaces as, ‘A landmark in the history of general topology’. In this book, the author has expanded this study further and taken it in a new and exciting direction. The number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, both for approach spaces and for uniform gauge spaces, as well as compactifications for approach spaces is performed. A paradigm shift is created by the new concept of index analysis. Making use of the rich intrinsic quantitative information present in approach structures, a technique is developed whereby indices are defined that measure the extent to which properties hold, and theorems become inequalities involving indices; therefore vastly extending the realm of applicability of many classical results. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory. Finally a comprehensive analysis is made concerning the categorical aspects of the theory and its links with other topological categories. Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science.
Download or read book Algebraic Geometric Topology written by and published by . This book was released on 2007 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theoretical Aspects of Computing ICTAC 2023 written by Erika Ábrahám and published by Springer Nature. This book was released on 2023-12-24 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 20th International Colloquium on Theoretical Aspects of Computing, ICTAC 2023, which took place in Lima, Peru, during December 4–8, 2023. The 20 full papers presented in this volume together with 3 invited papers and 1 tool paper were carefully reviewed and selected from 40 submissions. They were organised in the topical sections as follows: Bring Together Practitioners; Researchers from Academia; Industry; Government to Present Research Results and Exchange Experience and Ideas.
Download or read book Coalgebraic Methods in Computer Science written by Barbara König and published by Springer Nature. This book was released on with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Download or read book Recent Progress in General Topology written by M. Husek and published by North Holland. This book was released on 1992-11-20 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan, North-Holland, 1984), which gives an almost complete picture of the state of the art of Set Theoretic Topology before 1984. In the present volume several important developments are surveyed that surfaced in the period 1984-1991. This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990). Solutions to some of the original 1100 open problems are discussed and new problems are posed.
Download or read book Non Associative Normed Algebras Volume 2 Representation Theory and the Zel manov Approach written by Miguel Cabrera García and published by Cambridge University Press. This book was released on 2018-04-12 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.
Download or read book Logic Language Information and Computation written by Juliette Kennedy and published by Springer. This book was released on 2017-07-10 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 24th Workshop on Logic, Language, Information and Communication, WoLLIC 2017, held in London, UK, in August 2017. The 28 contributed papers were carefully reviewed and selected from 61 submissions. They cover interdisciplinary research in pure and applied logic, aiming at interactions between logic and the sciences related to information and computation.
Download or read book Algebraic Topology old and New written by Marek Golasiński and published by . This book was released on 2009 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Analysis of Random Walks Light Tailed Distributions written by A.A. Borovkov and published by Cambridge University Press. This book was released on 2020-10-29 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic modern treatise on large deviation theory for random walks with light tails, from one of its key creators.
Download or read book Asymptotic Analysis of Random Walks written by A. A. Borovkov and published by Cambridge University Press. This book was released on 2020-10-29 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.
Download or read book Equivalents of the Riemann Hypothesis written by Kevin Broughan and published by Cambridge University Press. This book was released on 2017-11-02 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume of two presents classical and modern arithmetic equivalents to the Riemann hypothesis. Accompanying software is online.
Download or read book Quasi Hopf Algebras written by Daniel Bulacu and published by Cambridge University Press. This book was released on 2019-02-21 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
