**The Classification Theorem for Compact Surfaces**

by Jean Gallier, Dianna Xu

2009**Number of pages**: 134

**Description**:

The topic of this book is the classification theorem for compact surfaces. We present the technical tools needed for proving rigorously the classification theorem, give a detailed proof using these tools, and also discuss the history of the theorem and its various "proofs".

Download or read it online for free here:

**Download link**

(multiple PDF files)

## Similar books

**Topology Lecture Notes**

by

**Thomas Ward**-

**UEA**

Contents: Topological and Metric Spaces, Homotopy Exquivalence, Fundamental Groups, Covering Spaces and Applications, Classification of Surfaces, Simplicial Complexes and Homology Groups, Homology Calculations, Simplicial Approximation, etc.

(

**11626**views)

**Differential Forms and Cohomology: Course**

by

**Peter Saveliev**-

**Intelligent Perception**

Differential forms provide a modern view of calculus. They also give you a start with algebraic topology in the sense that one can extract topological information about a manifold from its space of differential forms. It is called cohomology.

(

**8288**views)

**A Topology Primer**

by

**Klaus Wirthmüller**-

**Technische Universität Kaiserslautern**

The purpose of this text is to make familiar with the basics of topology, to give a concise introduction to homotopy, and to make students familiar with homology. Readers are expected to have knowledge of analysis and linear algebra.

(

**12699**views)

**The Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres**

by

**Paul Goerss**-

**Northwestern University**

Contents: The Adams spectral sequence; Classical calculations; The Adams-Novikov Spectral Sequence; Complex oriented homology theories; The height filtration; The chromatic decomposition; Change of rings; The Morava stabilizer group.

(

**11527**views)