**Graduate Studies in Mathematics**

Volume: 208;
2020;
408 pp;
Softcover

MSC: Primary 57; 53; 55; 30;

**Print ISBN: 978-1-4704-6132-4
Product Code: GSM/208**

List Price: $89.00

AMS Member Price: $71.20

MAA Member Price: $80.10

**Electronic ISBN: 978-1-4704-6162-1
Product Code: GSM/208.E**

List Price: $89.00

AMS Member Price: $71.20

MAA Member Price: $80.10

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#### Supplemental Materials

# Geometry and Topology of Manifolds: Surfaces and Beyond

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*Vicente Muñoz; Ángel González-Prieto; Juan Ángel Rojo*

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 Sociedad Matemática Española (RSME)

#### Readership

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