Topology and Geometry - Info and Reading Options

"Topology and Geometry" Table Of Contents:

• 1- General Topology
• 2- Metric Spaces
• 3- Topological Spaces
• 4- Subspaces
• 5- Connectivity and Components
• 6- Separation Axioms
• 7- Nets (Moore-Smith Convergence)*
• 8- Compactness
• 9- Products
• 10- Metric Spaces Again
• 11- Existence of Real Valued Functions
• 12- Locally Compact Spaces
• 13- Paracompact Spaces
• 14- Quotient Spaces
• 15- Homotopy
• 16- Topological Groups
• 17- Convex Bodies
• 18- The Baire Category Theorem
• 19- Diferentiable Manifolds
• 20- The Implicit Function Theorem
• 21- Differentiable Manifolds
• 22- Local Coordinates
• 23- Induced Structures and Examples
• 24- Tangent Vectors and Differentials
• 25- Sard's Theorem and Regular Values
• 26- Local Properties of Immersions and Submersions
• 27- Vector Fields and Flows
• 28- Tangent Bundles
• 29- Embedding in Euclidean Space
• 30- Tubular Neighborhoods and Approximations
• 31- Classical Lie Groups*
• 32- Fiber Bundles*
• 33- Induced Bundles and Whitney Sums*
• 34- Transversality*
• 35- Thom-Pontryagin Theory*
• 36- Fundamental Group
• 37- Homotopy Groups
• 38- The Fundamental Group
• 39- Covering Spaces
• 40- The Lifting Theorem
• 41- The Action of π_1 on the Fiber
• 42- Deck Transformations
• 43- Properly Discontinuous Actions
• 44- Classification of Covering Spaces
• 45- The Seifert-Van Kampen Theorem*
• 46- Remarks on SO(3)*
• 47- Homology Theory
• 48- Homology Groups
• 49- The Zeroth Homology Group
• 50- The First Homology Group
• 51- Functorial Properties
• 52- Homological Algebra
• 53- Axioms for Homology
• 54- Computation of Degrees
• 55- CW-Complexes
• 56- Conventions for CW-Complexes
• 57- Cellular Homology
• 58- Cellular Maps
• 59- Products of CW-Complexes*
• 60- Euler's Formula
• 61- Homology of Real Projective Space
• 62- Singular Homology
• 63- The Cross Product
• 64- Subdivision
• 65- The Mayer-Victoris Sequence
• 66- The Generalized Jordan Curve Theorem
• 67- The Borsuk-Ulam Theorem
• 68- Simplicial Complexes
• 69- Simplicial Maps
• 70- The Lefschetz-Hopf Fixed Point Theorem
• 71- Cohomology
• 72- Multilinear Algebra
• 73- Differential Forms
• 74- Integration of Forms
• 75- Stokes' Theorem
• 76- Relationship to Singular Homology
• 77- More Homological Algebra
• 78- Universal Coefficient Theorems
• 79- Excision and Homotopy
• 80- de Rham's Theorem
• 81- The de Rham Theory of CP^n*
• 82- Hopf's Theorem on Maps to Spheres*
• 83- Differential Forms on Compact Lie Groups*
• 84- Products and Duality
• 85- The Cross Product and the Künneth Theorem
• 86- A Sign Convention
• 87- The Cohomology Cross Product
• 88- The Cup Product
• 89- The Cap Product
• 90- Classical Outlook on Duality*
• 91- The Orientation Bundle
• 92- Duality Theorems
• 93- Duality on Compact Manifolds with Boundary
• 94- Applications of Duality
• 95- Intersection Theory*
• 96- The Euler Class, Lefschetz Numbers, and Vector Fields*
• 97- The Gysin Sequence*
• 98- Lefschetz Coincidence Theory*
• 99- Steenrod Operations*
• 100- Construction of the Steenrod Squares*
• 101- Stiefel-Whitney Classes*
• 102- Plumbing*
• 103- Homotopy Theory
• 104- Cofibrations
• 105- The Compact-Open Topology
• 106- H-Spaces, H-Groups, and H-Cogroups
• 107- Homotopy Groups
• 108- The Homotopy Sequence of a Pair
• 109- Fiber Spaces
• 110- Free Homotopy
• 111- Classical Groups and Associated Manifolds
• 112- The Homotopy Addition Theorem
• 113- The Hurewicz Theorem
• 114- The Whitehead Theorem
• 115- Eilenberg-Mac Lane Spaces
• 116- Obstruction Theory*
• 117- Obstruction Cochains and Vector Bundles*
• 118- Appendices
• 119- The Additivity Axiom
• 120- Background in Set Theory
• 121- Critical Values
• 122- Direct Limits
• 123- Euclidean Neighbouhood Retracts

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