Ordered Groups And Topology PDF Download
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Author | : Adam J. Clay |
Publisher | : |
Total Pages | : |
Release | : 2016 |
Genre | : MATHEMATICS |
ISBN | : 9781470435622 |
Download Ordered Groups and Topology Book in PDF, ePub and Kindle
This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book w.
Author | : Adam Clay |
Publisher | : American Mathematical Soc. |
Total Pages | : 167 |
Release | : 2016-11-16 |
Genre | : Mathematics |
ISBN | : 1470431068 |
Download Ordered Groups and Topology Book in PDF, ePub and Kindle
This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
Author | : M. Pouzet |
Publisher | : Elsevier |
Total Pages | : 599 |
Release | : 1984-01-01 |
Genre | : Mathematics |
ISBN | : 0080872107 |
Download Orders: Description and Roles Book in PDF, ePub and Kindle
Orders: Description and Roles
Author | : Leopoldo Nachbin |
Publisher | : |
Total Pages | : 132 |
Release | : 1965 |
Genre | : Topology |
ISBN | : |
Download Topology and Order Book in PDF, ePub and Kindle
Author | : V.M. Kopytov |
Publisher | : Springer Science & Business Media |
Total Pages | : 408 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401583048 |
Download The Theory of Lattice-Ordered Groups Book in PDF, ePub and Kindle
A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way. These connections were established in the period between the end of 19th and beginning of 20th century. It was realized that ordered algebraic systems occur in various branches of mathemat ics bound up with its fundamentals. For example, the classification of infinitesimals resulted in discovery of non-archimedean ordered al gebraic systems, the formalization of the notion of real number led to the definition of ordered groups and ordered fields, the construc tion of non-archimedean geometries brought about the investigation of non-archimedean ordered groups and fields. The theory of partially ordered groups was developed by: R. Dedekind, a. Holder, D. Gilbert, B. Neumann, A. I. Mal'cev, P. Hall, G. Birkhoff. These connections between partial order and group operations allow us to investigate the properties of partially ordered groups. For exam ple, partially ordered groups with interpolation property were intro duced in F. Riesz's fundamental paper [1] as a key to his investigations of partially ordered real vector spaces, and the study of ordered vector spaces with interpolation properties were continued by many functional analysts since. The deepest and most developed part of the theory of partially ordered groups is the theory of lattice-ordered groups. In the 40s, following the publications of the works by G. Birkhoff, H. Nakano and P.
Author | : Max Dehn |
Publisher | : Springer Science & Business Media |
Total Pages | : 404 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461246687 |
Download Papers on Group Theory and Topology Book in PDF, ePub and Kindle
The work of Max Dehn (1878-1952) has been quietly influential in mathematics since the beginning of the 20th century. In 1900 he became the first to solve one of the famous Hilbert problems (the third, on the decomposition of polyhedra), in 1907 he collaborated with Heegaard to produce the first survey of topology, and in 1910 he began publishing his own investigations in topology and combinatorial group theory. His influence is apparent in the terms Dehn's algorithm, Dehn's lemma and Dehn surgery (and Dehnsche Gruppenbilder, generally known in English as Cayley diagrams), but direct access to his work has been difficult. No edition of his works has been produced, and some of his most important results were never published, at least not by him. The present volume is a modest attempt to bring Dehn's work to a wider audience, particularly topologists and group theorists curious about the origins of their subject and interested in mining the sources for new ideas. It consists of English translations of eight works : five of Dehn's major papers in topology and combinatorial group theory, and three unpublished works which illuminate the published papers and contain some results not available elsewhere. In addition, I have written a short introduction to each work, summarising its contents and trying to establish its place among related works of Dehn and others, and I have added an appendix on the Dehn-Nielsen theorem (often known simply as Nielsen's theorem) .
Author | : Maurice Pouzet |
Publisher | : |
Total Pages | : 548 |
Release | : 1984 |
Genre | : Ordered sets |
ISBN | : |
Download Orders : Description and Roles in Set Theory, Lattices, Ordered Groups, Topology, Theory of Models and Relations, Combinatorics, Effectiveness, Social Sciences Book in PDF, ePub and Kindle
Author | : M.E Anderson |
Publisher | : Springer Science & Business Media |
Total Pages | : 197 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 9400928718 |
Download Lattice-Ordered Groups Book in PDF, ePub and Kindle
The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].
Author | : Robert Lewis Madell |
Publisher | : |
Total Pages | : 204 |
Release | : 1968 |
Genre | : |
ISBN | : |
Download Topological Lattice Ordered Groups Book in PDF, ePub and Kindle
Author | : Taqdir Husain |
Publisher | : Courier Dover Publications |
Total Pages | : 241 |
Release | : 2018-02-15 |
Genre | : Mathematics |
ISBN | : 0486819191 |
Download Introduction to Topological Groups Book in PDF, ePub and Kindle
Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.