Coverings Of Profinite Graphs
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Coverings Of Profinite Graphs
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Author : Amrita Acharyya
language : en
Publisher:
Release Date : 2013
Coverings Of Profinite Graphs written by Amrita Acharyya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Electronic dissertations categories.
We define a covering of a profinite graph to be a projective limit of a system of covering maps of finite graphs. With this notion of covering, we develop a covering theory for profinite graphs which is in many ways analogous to the classical theory of coverings of abstract graphs. For example, it makes sense to talk about the universal cover of a profinite graph and we show that it always exists and is unique. We define the profinite fundamental group of a profinite graph and show that a connected cover of a connected profinite graph is the universal cover if and only if its profinite fundamental group is trivial.
Profinite Graphs And Groups
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Author : Luis Ribes
language : en
Publisher: Springer
Release Date : 2017-08-23
Profinite Graphs And Groups written by Luis Ribes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-23 with Mathematics categories.
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open questions and suggestions for further reading.
Graphs Groups And Surfaces
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Author : A.T. White
language : en
Publisher: Elsevier
Release Date : 1985-01-01
Graphs Groups And Surfaces written by A.T. White and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing. Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'' and 9 as ``unsolved''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''.
Proceedings Of The International Conference On Algebra Dedicated To The Memory Of A I Mal Cev
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Author : Leonid A. Bokut'
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Proceedings Of The International Conference On Algebra Dedicated To The Memory Of A I Mal Cev written by Leonid A. Bokut' 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 1992 with Algebra categories.
Field Arithmetic
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Author : Michael D. Fried
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Field Arithmetic written by Michael D. Fried and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?
Cofinite Graphs And Their Profinite Completions
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Author : Bikash Chandra Das
language : en
Publisher:
Release Date : 2013
Cofinite Graphs And Their Profinite Completions written by Bikash Chandra Das and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Electronic dissertations categories.
We generalize the work of B. Hartley, to the category of topological graphs. The completion of a topological group in Hartley's work can be thought of as a particular example of the completion of a general uniform space. We consider topologies that are induced by uniformities, in order to topologize our graph structures and talk about their completions. In this dissertation generalize the idea of cofinite groups, due to B. Hartley. First we define cofinite spaces in general. Then, as a special case, we study cofinite graphs and their uniform completions. We are able to show that these completions are also cofinite graphs and being compact Hausdorff and totally disconnected they are rather regarded as profinite graphs. The idea of constructing a cofinite graph starts with defining a uniform topological graph in an appropriate fashion. We endow abstract graphs with uniformities corresponding to separating filter bases of equivalence relations with finitely many equivalence classes over the graph. By taking finitely many equivalence classes, we want to ensure the production of profinite structures over our topological graphs on taking the projective limit of the corresponding quotient graphs. It is established that for any cofinite graph there exists a unique cofinite completion. Generalizing Hartley's idea of cofinite groups and obtaining the structure for cofinite graphs we start establishing a parallel theory of cofinite graphs which in many ways can also be thought of as generalizations of the well-known works on pronite graphs by Pavel Zalesskii and Luis Ribes. Suitably defining the concept of cofinite connectedness of a cofinite graph we find that many of the properties of connectedness of topological spaces have analogs for cofinite connectedness. As an immediate consequence we obtain the following generalized characterization of the connected Cayley graphs of conite groups: G be a cofinite group, X be a cofinite space, then Cayley graph (G, X) is also cofinite graph and it is cofinitely connected if and only if X generates G (topologically). Our immediate next concern is developing group actions on cofinite graphs. Defining the action of an abstract group over a cofinite graph in the most natural way we are able to characterize a unique way of uniformizing an abstract group with a cofinite structure, obtained from the cofinite structure of the graph in the underlying action, so that the afore said action becomes uniformly continuous. We show that the aforesaid actions can actually be extended to the structures' of corresponding cofinite completions, preserving the underlying character of the original group action.
Leningrad Mathematical Journal
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Author :
language : en
Publisher:
Release Date : 1990
Leningrad Mathematical Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Algebra categories.
What S Next
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Author : Dylan Thurston
language : en
Publisher: Princeton University Press
Release Date : 2020-07-07
What S Next written by Dylan Thurston and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-07 with Mathematics categories.
William Thurston (1946-2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of mathematical fields, from foliations, contact structures, and Teichm ller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. What's Next? brings together many of today's leading mathematicians to describe recent advances and future directions inspired by Thurston's transformative ideas. Including valuable insights from his colleagues and former students, What's Next? discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. This incisive and wide-ranging book also explores how he introduced new ways of thinking about and doing mathematics, innovations that have had a profound and lasting impact on the mathematical community as a whole.
Ischia Group Theory 2008 Proceedings Of The Conference In Group Theory
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Author : Mariagrazia Bianchi
language : en
Publisher: World Scientific
Release Date : 2009-07-30
Ischia Group Theory 2008 Proceedings Of The Conference In Group Theory written by Mariagrazia Bianchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-30 with Mathematics categories.
The volume contains a collection of research articles by leading experts in group theory, and reports of several accessible surveys of recent research in the area. The compilation provide an overview of the diversity of themes and applications that interest today's group theorists. The topics covered in this volume include: character theory, combinatorial group theory, varieties of groups, conjugacy classes, profinite groups, graphs connected with groups, subgroup structure, representation theory.
Collected Works Of William P Thurston With Commentary
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Author : Benson Farb
language : en
Publisher: American Mathematical Society
Release Date : 2023-06-02
Collected Works Of William P Thurston With Commentary written by Benson Farb and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-02 with Mathematics categories.
William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume II contains William Thurston's papers on the geometry and topology of 3-manifolds, on complexity, constructions and computers, and on geometric group theory.