Ordered Groups And Topology
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Author |
: Adam Clay |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 167 |
Release |
: 2016-11-16 |
ISBN-10 |
: 9781470431068 |
ISBN-13 |
: 1470431068 |
Rating |
: 4/5 (68 Downloads) |
Synopsis Ordered Groups and Topology by : Adam Clay
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 |
: Adam J. Clay |
Publisher |
: |
Total Pages |
: |
Release |
: 2016 |
ISBN-10 |
: 1470435624 |
ISBN-13 |
: 9781470435622 |
Rating |
: 4/5 (24 Downloads) |
Synopsis Ordered Groups and Topology by : Adam J. Clay
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 |
: M.E Anderson |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 197 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9789400928718 |
ISBN-13 |
: 9400928718 |
Rating |
: 4/5 (18 Downloads) |
Synopsis Lattice-Ordered Groups by : M.E Anderson
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 |
: Andrew H. Wallace |
Publisher |
: Courier Corporation |
Total Pages |
: 290 |
Release |
: 2007-01-01 |
ISBN-10 |
: 9780486462394 |
ISBN-13 |
: 0486462390 |
Rating |
: 4/5 (94 Downloads) |
Synopsis Algebraic Topology by : Andrew H. Wallace
Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.
Author |
: V.M. Kopytov |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 408 |
Release |
: 2013-03-09 |
ISBN-10 |
: 9789401583046 |
ISBN-13 |
: 9401583048 |
Rating |
: 4/5 (46 Downloads) |
Synopsis The Theory of Lattice-Ordered Groups by : V.M. Kopytov
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 |
: Roberta Botto Mura |
Publisher |
: |
Total Pages |
: 175 |
Release |
: 1977 |
ISBN-10 |
: 0608089672 |
ISBN-13 |
: 9780608089676 |
Rating |
: 4/5 (72 Downloads) |
Synopsis Orderable Groups by : Roberta Botto Mura
Author |
: J. P. May |
Publisher |
: University of Chicago Press |
Total Pages |
: 262 |
Release |
: 1999-09 |
ISBN-10 |
: 0226511839 |
ISBN-13 |
: 9780226511832 |
Rating |
: 4/5 (39 Downloads) |
Synopsis A Concise Course in Algebraic Topology by : J. P. May
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Author |
: M. Pouzet |
Publisher |
: Elsevier |
Total Pages |
: 599 |
Release |
: 1984-01-01 |
ISBN-10 |
: 9780080872100 |
ISBN-13 |
: 0080872107 |
Rating |
: 4/5 (00 Downloads) |
Synopsis Orders: Description and Roles by : M. Pouzet
Orders: Description and Roles
Author |
: Bernd Schröder |
Publisher |
: Birkhäuser |
Total Pages |
: 426 |
Release |
: 2016-05-11 |
ISBN-10 |
: 9783319297880 |
ISBN-13 |
: 3319297880 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Ordered Sets by : Bernd Schröder
An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.
Author |
: Warren Page |
Publisher |
: Courier Dover Publications |
Total Pages |
: 398 |
Release |
: 1988 |
ISBN-10 |
: 0486658082 |
ISBN-13 |
: 9780486658087 |
Rating |
: 4/5 (82 Downloads) |
Synopsis Topological Uniform Structures by : Warren Page
Exceptionally smooth, clear, detailed examination of uniform spaces, topological groups, topological vector spaces, topological algebras and abstract harmonic analysis. Also, topological vector-valued measure spaces as well as numerous problems and examples. For advanced undergraduates and beginning graduate students. Bibliography. Index.