18.905 | Fall 2016 | Graduate

Algebraic Topology I

Lecture Notes

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Algebraic Topology I: Lecture Notes
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Algebraic Topology I: Lecture 1 Introduction: Singular Simplices and Chains
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Algebraic Topology I: Lecture 2 Homology
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Algebraic Topology I: Lecture 3 Categories, Functors, Natural Transformations
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Algebraic Topology I: Lecture 4 Categorical Language
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Algebraic Topology I: Lecture 5 Homotopy, Star-shaped Regions
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Algebraic Topology I: Lecture 6 Homotopy Invariance of Homology
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Algebraic Topology I: Lecture 7 Homology Cross Product
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Algebraic Topology I: Lecture 8 Relative Homology
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Algebraic Topology I: Lecture 10 Excision and Applications
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Algebraic Topology I: Lecture 11 The Eilenberg Steenrod Axioms and the Locality Principle
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Algebraic Topology I: Lecture 12 Subdivision
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Algebraic Topology I: Lecture 13 Proof of the Locality Principle
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Algebraic Topology I: Lecture 14 CW-Complexes
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Algebraic Topology I: Lecture 15 CW-Complexes II
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Algebraic Topology I: Lecture 16 Homology of CW-Complexes
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Algebraic Topology I: Lecture 17 Real Projective Space
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Algebraic Topology I: Lecture 18 Euler Characteristic and Homology Approximation
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Algebraic Topology I: Lecture 19 Coefficients
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Algebraic Topology I: Lecture 20 Tensor Product
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Algebraic Topology I: Lecture 21 Tensor and Tor
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Algebraic Topology I: Lecture 22 The Fundamental Theorem of Homological Algebra
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Algebraic Topology I: Lecture 23 Hom and Lim
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Algebraic Topology I: Lecture 24 Universal Coefficient Theorem
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Algebraic Topology I: Lecture 25 Künneth and Eilenberg-Zilber
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Algebraic Topology I: Lecture 26 Coproducts, Cohomology
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Algebraic Topology I: Lecture 27 Ext and UCT
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Algebraic Topology I: Lecture 27 Products in Cohomology
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Algebraic Topology I: Lecture 29 Cup Product (cont.)
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Algebraic Topology I: Lecture 30 Surfaces and Nondegenerate Symmetric Bilinear Forms
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Algebraic Topology I: Lecture 31 Local Coefficients and Orientations
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Algebraic Topology I: Lecture 32 Proof of the Orientation Theorem
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Algebraic Topology I: Lecture 33 A Plethora of Products
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Algebraic Topology I: Lecture 34 Cap Product and “Cech” Cohomology
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Algebraic Topology I: Lecture 35 Cech Cohomology as a Cohomology Theory
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Algebraic Topology I: Lecture 36 The Fully Relative Cap Product
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Algebraic Topology I: Lecture 37 Poincaré Duality
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Algebraic Topology I: Lecture 38 Applications

Course Info

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Departments

As Taught In

Fall 2016

Level

Graduate

Topics

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