An error was encountered while trying to add the item to the cart. Please try again.
Copy To Clipboard
Successfully Copied!
Geometry and Topology of Manifolds: Surfaces and Beyond

Vicente Muñoz Universidad de Málaga, Málaga, Spain
Available Formats:
Softcover ISBN: 978-1-4704-6132-4
Product Code: GSM/208
List Price: $89.00 MAA Member Price:$80.10
AMS Member Price: $71.20 Electronic ISBN: 978-1-4704-6162-1 Product Code: GSM/208.E List Price:$89.00
MAA Member Price: $80.10 AMS Member Price:$71.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $133.50 MAA Member Price:$120.15
AMS Member Price: $106.80 Click above image for expanded view Geometry and Topology of Manifolds: Surfaces and Beyond Vicente Muñoz Universidad de Málaga, Málaga, Spain Ángel González-Prieto Universidad Politécnica de Madrid, Madrid, Spain Juan Ángel Rojo Universidad Politécnica de Madrid, Madrid, Spain Available Formats:  Softcover ISBN: 978-1-4704-6132-4 Product Code: GSM/208  List Price:$89.00 MAA Member Price: $80.10 AMS Member Price:$71.20
 Electronic ISBN: 978-1-4704-6162-1 Product Code: GSM/208.E
 List Price: $89.00 MAA Member Price:$80.10 AMS Member Price: $71.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$133.50 MAA Member Price: $120.15 AMS Member Price:$106.80
• Book Details

Volume: 2082020; 408 pp
MSC: Primary 57; 53; 55; 30;

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.

This book is published in cooperation with Real Sociedád Matematica Española.

Undergraduate and graduate students interested in teaching and learning the basics of algebraic and differential topology.

• Chapters
• Topological surfaces
• Algebraic topology
• Riemannian geometry
• Constant curvature
• Complex geometry
• Global analysis

• Reviews

• The book should be well-suited for several types of graduate-level geometry courses: The material encompasses manifolds and categories; the basics of homotopy, singular homology, and de Rham cohomology; Riemannian metrics, curvature and uniformization; holomorphic structures; and enough global analysis for Hodge theory, the existence of metrics of constant Gaussian curvature, and basic curvature flow. Each chapter provides useful supplementary reading, from textbooks to original papers, and contains numerous exercises of varying levels of difficulty. There is an extensive index and a comprehensive table of notation indexed by the page where notation first appears.

...The authors provide proofs of results, such as triangulation of surfaces, that in other textbooks are often outsourced, and they provide detailed references for results they do not prove. They have also made an effort to draw 'cultural links' between disparate parts of the material, the way a good instructor might.

Andrew D. Hwang, College of the Holy Cross
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2082020; 408 pp
MSC: Primary 57; 53; 55; 30;

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.

This book is published in cooperation with Real Sociedád Matematica Española.

Undergraduate and graduate students interested in teaching and learning the basics of algebraic and differential topology.

• Chapters
• Topological surfaces
• Algebraic topology
• Riemannian geometry
• Constant curvature
• Complex geometry
• Global analysis
• The book should be well-suited for several types of graduate-level geometry courses: The material encompasses manifolds and categories; the basics of homotopy, singular homology, and de Rham cohomology; Riemannian metrics, curvature and uniformization; holomorphic structures; and enough global analysis for Hodge theory, the existence of metrics of constant Gaussian curvature, and basic curvature flow. Each chapter provides useful supplementary reading, from textbooks to original papers, and contains numerous exercises of varying levels of difficulty. There is an extensive index and a comprehensive table of notation indexed by the page where notation first appears.

...The authors provide proofs of results, such as triangulation of surfaces, that in other textbooks are often outsourced, and they provide detailed references for results they do not prove. They have also made an effort to draw 'cultural links' between disparate parts of the material, the way a good instructor might.

Andrew D. Hwang, College of the Holy Cross
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.