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Topology and geometry

Topology and geometry more books like this

by Glen E Bredon

This book is intended as a textbook for a first-year graduate course on algebraic topology, with as strong flavoring in smooth manifold theory. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. It covers most of the topics all ...

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Algebraic Topology

Algebraic Topology more books like this

by Allen Hatcher

In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and ...

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The Poincare Conjecture: In Search of the Shape of the Universe

The Poincare Conjecture: In Search of the Shape of the Universe more books like this

by Donal O'Shea

In telling this vibrant story, O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians.

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Differential Forms in Algebraic Topology

Differential Forms in Algebraic Topology more books like this

by Raoul Bott, Loring W Tu

This text, developed from a first-year graduate course in algebraic topology, is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas- de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes-and include some ...

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Algebraic and Differential Topology of Robust Stability

Algebraic and Differential Topology of Robust Stability more books like this

by Edmond A Jonckheere

In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology proceeding from an easily motivated control engineering problem, showing the relevance of advanced topological concepts and reconstructing the fundamental concepts of algebraic/differential ...

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A combinatorial introduction to topology

A combinatorial introduction to topology more books like this

by Michael Henle

The creation of algebraic topology is a major accomplishment of the 20th century. The goal of this book is to show how geometric and algebraic ideas met and grew together into an important branch of mathematics in the recent past. The book also conveys the fun and adventure that can be part of a mathematical investigation.

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A First Course in Algebraic Topology

A First Course in Algebraic Topology more books like this

by Czes Kosniowski

This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The ...

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Algebraic Topology: An Introduction

Algebraic Topology: An Introduction more books like this

by William S Massey

William S. Massey Professor Massey, born in Illinois in 1920, received his bachelor's degree from the University of Chicago and then served for four years in the U.S. Navy during World War II. After the War he received his Ph.D. from Princeton University and spent two additional years there as a post-doctoral research assistant. He then taught for ...

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Topology in Process Calculus: Approximate Correctness and Infinite Evolution of Concurrent Programs

Topology in Process Calculus: Approximate Correctness and Infinite Evolution of Concurrent Programs more books like this

by Mingsheng Ying

Communication and concurrency are essential in understanding complex dynamic systems, and there have been many theories to deal with them such as Petri nets, CSP and ACP. Among them, CCS (process calculus is one of the most important and mathematically developed models of communication and concurrency. Various behavior equivalences between agents, ...

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Algebraic Topology and Algebraic K-Theory: Proceedings of a Symposium in Honor of John C. Moore. (Am-113)

Algebraic Topology and Algebraic K-Theory: Proceedings of a Symposium in Honor of John C. Moore. (Am-113) more books like this

by William Browder (Editor), John C Moore

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Algebraic topology more books like this

by Edwin Henry Spanier

Intended for use both as a text and a reference, this book is an exposition of the fundamental ideas of algebraic topology. The first third of the book covers the fundamental group, its definition and its application in the study of covering spaces. The focus then turns to homology theory, including cohomology, cup products, cohomology operations, ...

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Lecture Notes on Elementary Topology and Geometry more books like this

by I M Singer, J a Thorpe

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Algebraic topology more books like this

by C. R. F. Maunder

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical ...

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A Basic Course in Algebraic Topology more books like this

by William S Massey

This book is intended to serve as a textbook for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unecessary ...

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An Introduction to Algebraic Topology more books like this

by Andrew H Wallace

This self-contained treatment assumes only some knowledge of real numbers and real analysis. The first three chapters focus on the basics of point-set topology, after which the text proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. Exercises form an integral part of the text. 1961 edition.

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Algebraic topology: homology and cohomology more books like this

by Andrew H Wallace

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Braids and Coverings: Selected Topics more books like this

by Vagn Lundsgaard Hansen

This book is based on a graduate course taught by the author at the University of Maryland, USA. The lecture notes have been revised and augmented by examples. The work falls into two strands. The first two chapters develop the elementary theory of Artin Braid groups both geometrically and via homotopy theory, and discuss the link between knot ...

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Algebraic Topology: A First Course more books like this

by Marvin J Greenberg

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Adams Memorial Symposium on Algebraic Topology: Volume 1 more books like this

by Nigel Ray (Editor), Grant Walker (Editor), N J Hitchin (Editor)

J. Frank Adams had a profound influence on algebraic topology, and his works continue to shape its development. The International Symposium on Algebraic Topology held in Manchester during July 1990 was dedicated to his memory, and virtually all of the world's leading experts took part. This two volume work constitutes the proceedings of the ...

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An Introduction to Algebraic Topology more books like this

by Joseph J Rotman

This book is a clear exposition, with exercises, of the basic ideas of algebraic topology: homology (singular, simplicial, and cellular), homotopy groups, and cohomology rings. It is suitable for a two-semester course at the beginning graduate level, requiring as a prerequisite a knowledge of point set topology and basic algebra. Although ...

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Geometric and Topological Methods for Quantum Field Theory more books like this

by Hernan Ocampo (Editor), Sylvie Paycha (Editor), Andres Vargas (Editor)

This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is ...

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Seminar on transformation groups more books like this

by A. Borel

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A Geometric Introduction to Topology more books like this

by Charles Terence Clegg Wall

First course in algebraic topology for advanced undergraduates. Homotopy theory, the duality theorem, relation of topological ideas to other branches of pure mathematics. Exercises and problems. 1972 edition.

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Abstract harmonic analysis more books like this

by Edwin Hewitt, Kenneth A Ross

This book is a continuation of vol. I (Grundlehren vol. 115, also available in softcover), and contains a detailed treatment of some important parts of harmonic analysis on compact and locally compact abelian groups. From the reviews: "This work aims at giving a monographic presentation of abstract harmonic analysis, far more complete and ...

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The algebraic characterization of geometric 4-manifolds more books like this

by Hillman

This book describes work, largely that of the author, on the characterization of closed 4-manifolds in terms of familiar invariants such as Euler characteristic, fundamental group, and Stiefel-Whitney classes. Using techniques from homological group theory, the theory of 3-manifolds and topological surgery, infrasolvmanifolds are characterized up ...

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