Perspectives in Analysis, Geometry, and Topology

Perspectives in Analysis, Geometry, and Topology
Title Perspectives in Analysis, Geometry, and Topology PDF eBook
Author Ilia Itenberg
Publisher Springer Science & Business Media
Pages 487
Release 2011-12-13
Genre Mathematics
ISBN 0817682767

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The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

Perspectives in Analysis, Geometry, and Topology

Perspectives in Analysis, Geometry, and Topology
Title Perspectives in Analysis, Geometry, and Topology PDF eBook
Author Ilia Itenberg
Publisher Springer Science & Business Media
Pages 483
Release 2011-12-14
Genre Mathematics
ISBN 0817682775

Download Perspectives in Analysis, Geometry, and Topology Book in PDF, Epub and Kindle

The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

Geometry and Topology of Manifolds: Surfaces and Beyond

Geometry and Topology of Manifolds: Surfaces and Beyond
Title Geometry and Topology of Manifolds: Surfaces and Beyond PDF eBook
Author Vicente Muñoz
Publisher American Mathematical Soc.
Pages 408
Release 2020-10-21
Genre Education
ISBN 1470461323

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This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.

Manifolds, Sheaves, and Cohomology

Manifolds, Sheaves, and Cohomology
Title Manifolds, Sheaves, and Cohomology PDF eBook
Author Torsten Wedhorn
Publisher Springer
Pages 366
Release 2016-07-25
Genre Mathematics
ISBN 3658106336

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This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.

Geometrical Vectors

Geometrical Vectors
Title Geometrical Vectors PDF eBook
Author Gabriel Weinreich
Publisher University of Chicago Press
Pages 132
Release 1998-07-06
Genre Mathematics
ISBN 9780226890487

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Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject. Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition. Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.

Topology and Geometry for Physicists

Topology and Geometry for Physicists
Title Topology and Geometry for Physicists PDF eBook
Author Charles Nash
Publisher Courier Corporation
Pages 302
Release 2013-08-16
Genre Mathematics
ISBN 0486318362

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Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.

Topology

Topology
Title Topology PDF eBook
Author Tai-Danae Bradley
Publisher MIT Press
Pages 167
Release 2020-08-18
Genre Mathematics
ISBN 0262359626

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A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.