Combinatorial Topology

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Combinatorial Algebraic Topology

Author : Dimitry Kozlov
Publisher : Springer Science & Business Media
ISBN 13 : 9783540730514
Total Pages : 416 pages
Book Rating : 4.7/5 (35 download)

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Book Synopsis Combinatorial Algebraic Topology by : Dimitry Kozlov

Download or read book Combinatorial Algebraic Topology written by Dimitry Kozlov and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

A Combinatorial Introduction to Topology

Author : Michael Henle
Publisher : Courier Corporation
ISBN 13 : 9780486679662
Total Pages : 340 pages
Book Rating : 4.6/5 (796 download)

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Book Synopsis A Combinatorial Introduction to Topology by : Michael Henle

Download or read book A Combinatorial Introduction to Topology written by Michael Henle and published by Courier Corporation. This book was released on 1994-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

Distributed Computing Through Combinatorial Topology

Author : Maurice Herlihy
Publisher : Newnes
ISBN 13 : 0124047289
Total Pages : 335 pages
Book Rating : 4.1/5 (24 download)

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Book Synopsis Distributed Computing Through Combinatorial Topology by : Maurice Herlihy

Download or read book Distributed Computing Through Combinatorial Topology written by Maurice Herlihy and published by Newnes. This book was released on 2013-11-30 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributed Computing Through Combinatorial Topology describes techniques for analyzing distributed algorithms based on award winning combinatorial topology research. The authors present a solid theoretical foundation relevant to many real systems reliant on parallelism with unpredictable delays, such as multicore microprocessors, wireless networks, distributed systems, and Internet protocols. Today, a new student or researcher must assemble a collection of scattered conference publications, which are typically terse and commonly use different notations and terminologies. This book provides a self-contained explanation of the mathematics to readers with computer science backgrounds, as well as explaining computer science concepts to readers with backgrounds in applied mathematics. The first section presents mathematical notions and models, including message passing and shared-memory systems, failures, and timing models. The next section presents core concepts in two chapters each: first, proving a simple result that lends itself to examples and pictures that will build up readers' intuition; then generalizing the concept to prove a more sophisticated result. The overall result weaves together and develops the basic concepts of the field, presenting them in a gradual and intuitively appealing way. The book's final section discusses advanced topics typically found in a graduate-level course for those who wish to explore further. Named a 2013 Notable Computer Book for Computing Methodologies by Computing Reviews Gathers knowledge otherwise spread across research and conference papers using consistent notations and a standard approach to facilitate understanding Presents unique insights applicable to multiple computing fields, including multicore microprocessors, wireless networks, distributed systems, and Internet protocols Synthesizes and distills material into a simple, unified presentation with examples, illustrations, and exercises

Combinatorial Topology

Author : Pavel Sergeevich Aleksandrov
Publisher :
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Combinatorial Topology by : Pavel Sergeevich Aleksandrov

Download or read book Combinatorial Topology written by Pavel Sergeevich Aleksandrov and published by . This book was released on 1960 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Foundations of Combinatorial Topology

Author : L. S. Pontryagin
Publisher : Courier Corporation
ISBN 13 : 0486406857
Total Pages : 112 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Foundations of Combinatorial Topology by : L. S. Pontryagin

Download or read book Foundations of Combinatorial Topology written by L. S. Pontryagin and published by Courier Corporation. This book was released on 2015-05-20 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. A beneficial text for a graduate-level course, "this little book is an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette.

Intuitive Combinatorial Topology

Author : V.G. Boltyanskii
Publisher : Springer Science & Business Media
ISBN 13 : 1475756046
Total Pages : 153 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Intuitive Combinatorial Topology by : V.G. Boltyanskii

Download or read book Intuitive Combinatorial Topology written by V.G. Boltyanskii and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology is a relatively young and very important branch of mathematics, which studies the properties of objects that are preserved through deformations, twistings, and stretchings. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and well-motivated way. This book is well suited for readers who are interested in finding out what topology is all about.

Elements of Homology Theory

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
ISBN 13 : 0821838121
Total Pages : 418 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Elements of Homology Theory by : Viktor Vasilʹevich Prasolov

Download or read book Elements of Homology Theory written by Viktor Vasilʹevich Prasolov and published by American Mathematical Soc.. This book was released on 2007 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.

Classical Topology and Combinatorial Group Theory

Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 1461243726
Total Pages : 344 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Classical Topology and Combinatorial Group Theory by : John Stillwell

Download or read book Classical Topology and Combinatorial Group Theory written by John Stillwell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.

A Course in Topological Combinatorics

Author : Mark de Longueville
Publisher : Springer Science & Business Media
ISBN 13 : 1441979093
Total Pages : 246 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A Course in Topological Combinatorics by : Mark de Longueville

Download or read book A Course in Topological Combinatorics written by Mark de Longueville and published by Springer Science & Business Media. This book was released on 2013 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook in topological combinatorics covers such topics as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. Includes many figures and exercises.

Topology and Combinatorics of 3-Manifolds

Author : Klaus Johannson
Publisher : Springer
ISBN 13 : 3540491813
Total Pages : 464 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Topology and Combinatorics of 3-Manifolds by : Klaus Johannson

Download or read book Topology and Combinatorics of 3-Manifolds written by Klaus Johannson and published by Springer. This book was released on 2006-11-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds

Invitation to Combinatorial Topology

Author : Maurice Fréchet
Publisher : Courier Corporation
ISBN 13 : 0486147886
Total Pages : 148 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Invitation to Combinatorial Topology by : Maurice Fréchet

Download or read book Invitation to Combinatorial Topology written by Maurice Fréchet and published by Courier Corporation. This book was released on 2012-08-13 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: An elementary text that can be understood by anyone with a background in high school geometry, Invitation to Combinatorial Topology offers a stimulating initiation to important topological ideas. This translation from the original French does full justice to the text's coherent presentation as well as to its rich historical content. Subjects include the problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, and topological polygons. Considerations of the topological classification of closed surfaces cover elementary operations, use of normal forms of polyhedra, reduction to normal form, and application to the geometric theory of functions. 1967 edition. 108 figures. Bibliography. Index.

Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory

Author : Vassily Olegovich Manturov
Publisher : World Scientific
ISBN 13 : 9811220131
Total Pages : 387 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory by : Vassily Olegovich Manturov

Download or read book Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory written by Vassily Olegovich Manturov and published by World Scientific. This book was released on 2020-04-22 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups — Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.

Infinite-Dimensional Topology

Author : J. van Mill
Publisher : Elsevier
ISBN 13 : 0080933688
Total Pages : 401 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Infinite-Dimensional Topology by : J. van Mill

Download or read book Infinite-Dimensional Topology written by J. van Mill and published by Elsevier. This book was released on 1988-12-01 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed. One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.

Using the Borsuk-Ulam Theorem

Author : Jiri Matousek
Publisher : Springer Science & Business Media
ISBN 13 : 3540766499
Total Pages : 214 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Using the Borsuk-Ulam Theorem by : Jiri Matousek

Download or read book Using the Borsuk-Ulam Theorem written by Jiri Matousek and published by Springer Science & Business Media. This book was released on 2008-01-12 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: To the uninitiated, algebraic topology might seem fiendishly complex, but its utility is beyond doubt. This brilliant exposition goes back to basics to explain how the subject has been used to further our understanding in some key areas. A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. This book is the first textbook treatment of a significant part of these results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level. No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained.

Combinatorial Group Theory and Topology

Author : S. M. Gersten
Publisher : Princeton University Press
ISBN 13 : 9780691084107
Total Pages : 568 pages
Book Rating : 4.0/5 (841 download)

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Book Synopsis Combinatorial Group Theory and Topology by : S. M. Gersten

Download or read book Combinatorial Group Theory and Topology written by S. M. Gersten and published by Princeton University Press. This book was released on 1987-05-21 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work includes papers from a conference held in July 1984 at Alta Lodge, Utah. Contributors to the book include Roger Alperin, Hyman Bass, Max Benson, Joan S. Birman, Andrew J. Casson, Marshall Cohen, Donald J. Collins, Robert Craggs, Michael Dyer, Beno Eckmann, Stephen M. Gersten, Jane Gilman, Robert H. Gilman, Narain D. Gupta, John Hempel, James Howie, Roger Lyndon, Martin Lustig, Lee P. Neuwirth, Andrew J. Nicas, N. Patterson, John G. Ratcliffe, Frank Rimlinger, Caroline Series, John R. Stallings, C. W. Stark, and A. Royce Wolf.

Introduction to Combinatorial Torsions

Author : Vladimir Turaev
Publisher : Birkhäuser
ISBN 13 : 3034883218
Total Pages : 128 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Introduction to Combinatorial Torsions by : Vladimir Turaev

Download or read book Introduction to Combinatorial Torsions written by Vladimir Turaev and published by Birkhäuser. This book was released on 2012-12-06 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.

Geometric Combinatorics

Author : Ezra Miller
Publisher : American Mathematical Soc.
ISBN 13 : 0821837362
Total Pages : 705 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Combinatorics by : Ezra Miller

Download or read book Geometric Combinatorics written by Ezra Miller and published by American Mathematical Soc.. This book was released on 2007 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.