Combinatorial Methods In Topology And Algebraic Geometry

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Combinatorial Methods In Topology And Algebraic Geometry

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Author : John R. Harper
language : en
Publisher: American Mathematical Soc.
Release Date : 1985

Combinatorial Methods In Topology And Algebraic Geometry written by John R. Harper 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 1985 with Mathematics categories.

This collection marks the recent resurgence of interest in combinatorial methods, resulting from their deep and diverse applications both in topology and algebraic geometry. Nearly thirty mathematicians met at the University of Rochester in 1982 to survey several of the areas where combinatorial methods are proving especially fruitful: topology and combinatorial group theory, knot theory, 3-manifolds, homotopy theory and infinite dimensional topology, and four manifolds and algebraic surfaces. This material is accessible to advanced graduate students with a general course in algebraic topology along with some work in combinatorial group theory and geometric topology, as well as to established mathematicians with interests in these areas.For both student and professional mathematicians, the book provides practical suggestions for research directions still to be explored, as well as the aesthetic pleasures of seeing the interplay between algebra and topology which is characteristic of this field. In several areas the book contains the first general exposition published on the subject. In topology, for example, the editors have included M. Cohen, W. Metzler and K. Sauerman's article on 'Collapses of $K\times I$ and group presentations' and Metzler's 'On the Andrews-Curtis-Conjecture and related problems'. In addition, J. M. Montesino has provided summary articles on both 3 and 4-manifolds.

Combinatorial Algebraic Topology

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Author : Dimitry Kozlov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-24

Combinatorial Algebraic Topology written by Dimitry Kozlov 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 2007-10-24 with Mathematics categories.

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.

Combinatorial Methods In Topology And Algebraic Geometry

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1985

Combinatorial Methods In Topology And Algebraic Geometry written by 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 1985 with Combinatorial analysis categories.

Combinatorial Methods In Topology And Algebra

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Author : Bruno Benedetti
language : en
Publisher: Springer
Release Date : 2015-10-31

Combinatorial Methods In Topology And Algebra written by Bruno Benedetti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-31 with Mathematics categories.

Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.

Using The Borsuk Ulam Theorem

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Author : Jiri Matousek
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-04-17

Using The Borsuk Ulam Theorem written by Jiri Matousek 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 2003-04-17 with Computers categories.

"The textbook explains elementary but powerful topological methods based on the Borsuk-Ulam theorem and its generalizations. It covers many substantial results, sometimes with proofs simpler than those in the original papers. At the same time, it assumes no prior knowledge of algebraic topology, and all the required topological notions and results are gradually introduced. History, additional results, and references are presented in separate sections."--Résumé de l'éditeur.

Combinatorial Convexity And Algebraic Geometry

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Author : Günter Ewald
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Combinatorial Convexity And Algebraic Geometry written by Günter Ewald 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 2012-12-06 with Mathematics categories.

The aim of this book is to provide an introduction for students and nonspecialists to a fascinating relation between combinatorial geometry and algebraic geometry, as it has developed during the last two decades. This relation is known as the theory of toric varieties or sometimes as torus embeddings. Chapters I-IV provide a self-contained introduction to the theory of convex poly topes and polyhedral sets and can be used independently of any applications to algebraic geometry. Chapter V forms a link between the first and second part of the book. Though its material belongs to combinatorial convexity, its definitions and theorems are motivated by toric varieties. Often they simply translate algebraic geometric facts into combinatorial language. Chapters VI-VIII introduce toric va rieties in an elementary way, but one which may not, for specialists, be the most elegant. In considering toric varieties, many of the general notions of algebraic geometry occur and they can be dealt with in a concrete way. Therefore, Part 2 of the book may also serve as an introduction to algebraic geometry and preparation for farther reaching texts about this field. The prerequisites for both parts of the book are standard facts in linear algebra (including some facts on rings and fields) and calculus. Assuming those, all proofs in Chapters I-VII are complete with one exception (IV, Theorem 5.1). In Chapter VIII we use a few additional prerequisites with references from appropriate texts.

A Course In Topological Combinatorics

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Author : Mark de Longueville
language : en
Publisher: Springer Science & Business Media
Release Date : 2013

A Course In Topological Combinatorics written by Mark de Longueville 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 with Mathematics categories.

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.

Combinatorial Group Theory

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Author : Benjamin Fine
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

Combinatorial Group Theory written by Benjamin Fine 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 1990 with Mathematics categories.

Eighteen papers presented during a special AMS session designed to draw together researchers in various areas of infinite group theory, especially combinatorial group theory, to share methods and results.

Algebraic Geometry Sundance 1988

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Author : Brian Harbourne
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Algebraic Geometry Sundance 1988 written by Brian Harbourne 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 1991 with Mathematics categories.

This volume contains the proceedings of the NSF-CBMS Regional Conference on Algebraic Geometry, held in Sundance, Utah in July 1988. The conference focused on algebraic curves and related varieties. Some of the papers collected here represent lectures delivered at the conference, some report on research done during the conference, while others describe related work carried out elsewhere.

Topology And Geometry

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Author : Glen E. Bredon
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-06-24

Topology And Geometry written by Glen E. Bredon 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 1993-06-24 with Education categories.

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS