INTRODUCTION TO TOPOLOGICAL MANIFOLDS (GRADUATE TEXTS IN MATHEMATICS 202)
Written by John M. Lee
Published by Springer-Verlag
in 2000
ISBN: 0387950265
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INTRODUCTION TO TOPOLOGICAL MANIFOLDS (GRADUATE TEXTS IN MATHEMATICS 202)
Written by John M. Lee.
Stock no. 1830308
1st.
2000.
Softcover.
Very good condition.
An introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. A physical print-on-demand copy (printed by lightning Source UK Ltd). Yellow cardwraps. xvii and 385 pages including index. ISBN: 0387950265. Spine slightly faded and has vertical reading creases. Corners of covers lightly rubbed. Name in ink to front endpaper. A few minor marks to text block. Contents are clean.
Front cover
Contents
- 1 Introduction
- What are Manifolds?
- Why Study Manifolds?
- 2 Topological Spaces
- Topologies
- Bases
- Manifolds
- Problems
- 3 New Spaces from Old
- Subspaces
- Product Spaces
- Quotient Spaces
- Group Actions
- Problems
- 4 Connectedness and Compactness
- Connectedness
- Compactness
- Locally Compact Hausdorff Spaces
- Problems
- 5 Simplicial Complexes
- Euclidean Simplicial Complexes
- Abstract Simplicial Complexes
- Triangulation Theorems
- Orientations
- Combinatorial Invariants
- Problems
- 6 Curves and Surfaces
- Classification of Curves
- Surfaces
- Connected Sums
- Polygonal Presentations of Surfaces
- Classification of Surface Presentations
- Combinatorial Invariants
- Problems
- 7 Homotopy and the Fundamental Group
- Homotopy
- The Fundamental Group
- Homomorphisms Induced by Continuous Maps
- Homotopy Equivalence
- Higher Homotopy Groups
- Categories and Functors
- Problems
- 8 Circles and Spheres
- The Fundamental Group of the Circle
- Proofs of the Lifting Lemmas
- Fundamental Groups of Spheres
- Fundamental Groups of Product Spaces
- Fundamental Groups of Manifolds
- Problems
- 9 Some Group Theory
- Free Products
- Free Groups
- Presentations of Groups
- Free Abelian Groups
- Problems
- Distinguishing Manifolds
- Problems
- 11 Covering Spaces
- Definitions and Basic Properties
- Covering Maps and the Fundamental Group
- The Covering Group
- Problems
- 12 Classification of Coverings
- Covering Homomorphisms
- The Universal Covering Space
- Proper Group Actions
- The Classification Theorem
- Problems
- 13 Homology
- Singular Homology Groups
- Homotopy Invariance
- Homology and the Fundamental Group[
- The Mayer-Vietoris Theorem
- Applications
- The Homology of A Simplicial Complext
- Cohomology
- Problems
- References
- Index