A Guide To The Classification Theorem For Compact Surfaces

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A Guide to the Classification Theorem for Compact Surfaces

Author : Jean Gallier
Publisher : Springer Science & Business Media
ISBN 13 : 3642343643
Total Pages : 184 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis A Guide to the Classification Theorem for Compact Surfaces by : Jean Gallier

Download or read book A Guide to the Classification Theorem for Compact Surfaces written by Jean Gallier and published by Springer Science & Business Media. This book was released on 2013-02-05 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.

The Classification Theorem for Compact Surfaces

Author : Alexander Jasper
Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (119 download)

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Book Synopsis The Classification Theorem for Compact Surfaces by : Alexander Jasper

Download or read book The Classification Theorem for Compact Surfaces written by Alexander Jasper and published by . This book was released on 2014 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Surfaces

Author : The Open University
Publisher : The Open University
ISBN 13 :
Total Pages : 153 pages
Book Rating : 4./5 ( download)

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Book Synopsis Surfaces by : The Open University

Download or read book Surfaces written by The Open University and published by The Open University. This book was released on 2011-08-18 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 20-hour free course included the classification of surfaces, homeomorphism, orientability and the Euler characteristic.

The Classification of Compact Surfaces

Author : Nora Carol Hopkins
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.:/5 (358 download)

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Book Synopsis The Classification of Compact Surfaces by : Nora Carol Hopkins

Download or read book The Classification of Compact Surfaces written by Nora Carol Hopkins and published by . This book was released on 1978 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mostly Surfaces

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
ISBN 13 : 0821853686
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mostly Surfaces by : Richard Evan Schwartz

Download or read book Mostly Surfaces written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2011 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.

An Introduction to Topology

Author : Erik Christopher Zeeman
Publisher :
ISBN 13 :
Total Pages : 51 pages
Book Rating : 4.:/5 (15 download)

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Book Synopsis An Introduction to Topology by : Erik Christopher Zeeman

Download or read book An Introduction to Topology written by Erik Christopher Zeeman and published by . This book was released on 1966* with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonarchimedean and Tropical Geometry

Author : Matthew Baker
Publisher : Springer
ISBN 13 : 3319309455
Total Pages : 534 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Nonarchimedean and Tropical Geometry by : Matthew Baker

Download or read book Nonarchimedean and Tropical Geometry written by Matthew Baker and published by Springer. This book was released on 2016-08-18 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia. Topics covered in this volume include: Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons; The homotopy types of nonarchimedean analytifications; The existence of "faithful tropicalizations" which encode the topology and geometry of analytifications; Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves; Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory.

Geometry and topology of wild translation surfaces

Author : Randecker, Anja
Publisher : KIT Scientific Publishing
ISBN 13 : 3731504561
Total Pages : 162 pages
Book Rating : 4.7/5 (315 download)

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Book Synopsis Geometry and topology of wild translation surfaces by : Randecker, Anja

Download or read book Geometry and topology of wild translation surfaces written by Randecker, Anja and published by KIT Scientific Publishing. This book was released on 2016-04-28 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.

Computer Classification of Compact Surfaces

Author : Carl E. Zimmerman
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.:/5 (873 download)

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Book Synopsis Computer Classification of Compact Surfaces by : Carl E. Zimmerman

Download or read book Computer Classification of Compact Surfaces written by Carl E. Zimmerman and published by . This book was released on 1982 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Topology

Author : Smail Djebali
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111517780
Total Pages : 577 pages
Book Rating : 4.1/5 (115 download)

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Book Synopsis Algebraic Topology by : Smail Djebali

Download or read book Algebraic Topology written by Smail Djebali and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-11-18 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory. A simple approach based on point-set Topology is used throughout to introduce many standard constructions of fundamental and homological groups of surfaces and topological spaces. The approach does not rely on Homological Algebra. The constructions of some spaces using the quotient spaces such as the join, the suspension, and the adjunction spaces are developed in the setting of Topology only. The computations of the fundamental and homological groups of many surfaces and topological spaces occupy large parts of the book (sphere, torus, projective space, Mobius band, Klein bottle, manifolds, adjunctions spaces). Borsuk's theory of retracts which is intimately related to the problem of the extendability of continuous functions is developed in details. This theory together with the homotopy theory, the lifting and covering maps may serve as additional course material for students involved in General Topology. The book comprises 280 detailed worked examples, 320 exercises (with hints or references), 80 illustrative figures, and more than 80 commutative diagrams to make it more oriented towards applications (maps between spheres, Borsuk-Ulam Theory, Fixed Point Theorems, ...) As applications, the book offers some existence results on the solvability of some nonlinear differential equations subject to initial or boundary conditions. The book is suitable for students primarily enrolled in Algebraic Topology, General Topology, Homological Algebra, Differential Topology, Differential Geometry, and Topological Geometry. It is also useful for advanced undergraduate students who aspire to grasp easily some new concepts in Algebraic Topology and Applications. The textbook is practical both as a teaching and research document for Bachelor, Master students, and first-year PhD students since it is accessible to any reader with a modest understanding of topological spaces. The book aspires to fill a gap in the existing literature by providing a research and teaching document which investigates both the theory and the applications of Algebraic Topology in an accessible way without missing the main results of the topics covered.

Smooth Manifolds

Author : Claudio Gorodski
Publisher : Springer Nature
ISBN 13 : 3030497755
Total Pages : 162 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Smooth Manifolds by : Claudio Gorodski

Download or read book Smooth Manifolds written by Claudio Gorodski and published by Springer Nature. This book was released on 2020-08-01 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise and practical textbook presents the essence of the theory on smooth manifolds. A key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian manifolds in differential geometry; as space-times in general relativity; as phase spaces and energy levels in mechanics; as domains of definition of ODEs in dynamical systems; as Lie groups in algebra and geometry; and in many other areas. The book first presents the language of smooth manifolds, culminating with the Frobenius theorem, before discussing the language of tensors (which includes a presentation of the exterior derivative of differential forms). It then covers Lie groups and Lie algebras, briefly addressing homogeneous manifolds. Integration on manifolds, explanations of Stokes’ theorem and de Rham cohomology, and rudiments of differential topology complete this work. It also includes exercises throughout the text to help readers grasp the theory, as well as more advanced problems for challenge-oriented minds at the end of each chapter. Conceived for a one-semester course on Differentiable Manifolds and Lie Groups, which is offered by many graduate programs worldwide, it is a valuable resource for students and lecturers alike.

Philosophy and Model Theory

Author : Tim Button
Publisher : Oxford University Press
ISBN 13 : 0198790392
Total Pages : 534 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Philosophy and Model Theory by : Tim Button

Download or read book Philosophy and Model Theory written by Tim Button and published by Oxford University Press. This book was released on 2018 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.

Non-metrisable Manifolds

Author : David Gauld
Publisher : Springer
ISBN 13 : 9812872574
Total Pages : 214 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Non-metrisable Manifolds by : David Gauld

Download or read book Non-metrisable Manifolds written by David Gauld and published by Springer. This book was released on 2014-12-04 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds fall naturally into two classes depending on whether they can be fitted with a distance measuring function or not. The former, metrisable manifolds, and especially compact manifolds, have been intensively studied by topologists for over a century, whereas the latter, non-metrisable manifolds, are much more abundant but have a more modest history, having become of increasing interest only over the past 40 years or so. The first book on this topic, this book ranges from criteria for metrisability, dynamics on non-metrisable manifolds, Nyikos’s Bagpipe Theorem and whether perfectly normal manifolds are metrisable to structures on manifolds, especially the abundance of exotic differential structures and the dearth of foliations on the long plane. A rigid foliation of the Euclidean plane is described. This book is intended for graduate students and mathematicians who are curious about manifolds beyond the metrisability wall, and especially the use of Set Theory as a tool.

Diagrammatic Representation and Inference

Author : Peter Chapman
Publisher : Springer
ISBN 13 : 331991376X
Total Pages : 831 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Diagrammatic Representation and Inference by : Peter Chapman

Download or read book Diagrammatic Representation and Inference written by Peter Chapman and published by Springer. This book was released on 2018-06-07 with total page 831 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018, held in Edinburgh, UK, in June 2018. The 26 revised full papers and 28 short papers presented together with 32 posters were carefully reviewed and selected from 124 submissions. The papers are organized in the following topical sections: generating and drawing Euler diagrams; diagrams in mathematics; diagram design, principles and classification; reasoning with diagrams; Euler and Venn diagrams; empirical studies and cognition; Peirce and existential graphs; and logic and diagrams.

Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

Author : Jean H Gallier
Publisher : World Scientific
ISBN 13 : 9811245045
Total Pages : 799 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry by : Jean H Gallier

Download or read book Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry written by Jean H Gallier and published by World Scientific. This book was released on 2022-01-19 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.

Compact Complex Surfaces

Author : W. Barth
Publisher : Springer Science & Business Media
ISBN 13 : 364296754X
Total Pages : 315 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Compact Complex Surfaces by : W. Barth

Download or read book Compact Complex Surfaces written by W. Barth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Introduction. - Standard Notations. - Preliminaries. - Curves on Surfaces. - Mappings of Surfaces. - Some General Properties of Surfaces. - Examples. - The Enriques-Kodaira Classification. - Surfaces of General Type. - K3-Surfaces and Enriques Surfaces. - Bibliography. - Subject Index.

Topology

Author : Paul L. Shick
Publisher : John Wiley & Sons
ISBN 13 : 1118030583
Total Pages : 291 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Topology by : Paul L. Shick

Download or read book Topology written by Paul L. Shick and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors. Along with the standard point-set topology topics—connected and path-connected spaces, compact spaces, separation axioms, and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which "capstone" best suits his or her students. Topology: Point-Set and Geometric features: A short introduction in each chapter designed to motivate the ideas and place them into an appropriate context Sections with exercise sets ranging in difficulty from easy to fairly challenging Exercises that are very creative in their approaches and work well in a classroom setting A supplemental Web site that contains complete and colorful illustrations of certain objects, several learning modules illustrating complicated topics, and animations of particularly complex proofs