# Introduction to Topological Manifolds by John Lee

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## Main Question or Discussion Point

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[LIST]
[*] Preface
[*] Introduction
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[*] What Are Manifolds?
[*] Why Study Manifolds?
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[*] Topological Spaces
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[*] Topologies
[*] Convergence and Continuity
[*] Hausdorff Spaces
[*] Bases and Countability
[*] Manifolds
[*] Problems
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[*] New Spaces from Old
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[*] Subspaces
[*] Product Spaces
[*] Disjoint Union Spaces
[*] Quotient Spaces
[*] Topological Groups and Group Actions
[*] Problems
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[*] Connectedness and Compactness
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[*] Connectedness
[*] Compactness
[*] Local Compactness
[*] Paracompactness
[*] Proper Maps
[*] Problems
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[*] Cell Complexes
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[*] Cell Complexes and CW Complexes
[*] Topological Properties of CW Complexes
[*] Classification of 1-Dimensional Manifolds
[*] Simplicial Complexes
[*] Problems
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[*] Compact Surfaces
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[*] Surfaces
[*] Connected Sums of Surfaces
[*] Polygonal Presentations of Surfaces
[*] The Classification Theorem
[*] The Euler Characteristic
[*] Orientability
[*] Problems
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[*] Homotopy and the Fundamental Group
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[*] Homotopy
[*] The Fundamental Group
[*] Homomorphisms Induced by Continuous Maps
[*] Homotopy Equivalence
[*] Higher Homotopy Groups
[*] Categories and Functors
[*] Problems
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[*] The Circle
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[*] Lifting Properties of the Circle
[*] The Fundamental Group of the Circle
[*] Degree Theory for the Circle
[*] Problems
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[*] Some Group Theory
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[*] Free Products
[*] Free Groups
[*] Presentations of Groups
[*] Free Abelian Groups
[*] Problems
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[*] The Seifert–Van Kampen Theorem
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[*] Statement of the Theorem
[*] Applications
[*] Fundamental Groups of Compact Surfaces
[*] Proof of the Seifert–Van Kampen Theorem
[*] Problems
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[*] Covering Maps
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[*] Definitions and Basic Properties
[*] The General Lifting Problem
[*] The Monodromy Action
[*] Covering Homomorphisms
[*] The Universal Covering Space
[*] Problems
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[*] Group Actions and Covering Maps
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[*] The Automorphism Group of a Covering
[*] Quotients by Group Actions
[*] The Classification Theorem
[*] Proper Group Actions
[*] Problems
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[*] Homology
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[*] Singular Homology Groups
[*] Homotopy Invariance
[*] Homology and the Fundamental Group
[*] The Mayer–Vietoris Theorem
[*] Homology of Spheres
[*] Homology of CW Complexes
[*] Cohomology
[*] Problems
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[*] Appendix: Review of Set Theory
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[*] Basic Concepts
[*] Cartesian Products, Relations, and Function
[*] Number Systems and Cardinality
[*] Indexed Families
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[*] Appendix: Review of Metric Spaces
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[*] Euclidean Spaces
[*] Metrics
[*] Continuity and Convergence
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[*] Appendix: Review of Group Theory
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[*] Basic Definitions
[*] Cosets and Quotient Groups
[*] Cyclic Groups
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[*] Notation Index
[*] Subject Index
[*] References
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