Geometry and Topology of Manifolds

Surfaces and Beyond

Vicente Munoz, Angel Gonzalez-Preito, Juan Angel Rojo

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English

American Mathematical Society
30 November 2020

Geometry; Topology

Series: Graduate Studies in Mathematics

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.

By: Vicente Munoz, Angel Gonzalez-Preito, Juan Angel Rojo
Imprint: American Mathematical Society
Country of Publication: United States
Volume: 208
Dimensions: Height: 254mm, Width: 178mm,
Weight: 735g
ISBN: 9781470461324
ISBN 10: 1470461323
Series: Graduate Studies in Mathematics
Pages: 481
Publication Date: 30 November 2020
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Vicente Munoz, Universidad de Malaga, Spain, Angel Gonzalez-Preito, Universidad Politecnica de Madrid, Spain Juan Angel Rojo, Universidad Politecnica de Madrid, Spain.