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Algebraic Topology

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Author(s): O. Randal-Williams, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part III Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; geometry; topology; algebra; abstract algebra; modern algebra

Homotopy
Singular (co)homology
Chain complexes
Singular (co)homology
Four major tools of (co)homology
Homotopy invariance
Mayer-Vietoris
Relative homology
Excision theorem
Applications
Repaying the technical debt
Reduced homology
Cell complexes
(Co)homology with coefficients
Euler characteristic
Cup product
Kunneth theorem and universal coefficients theorem
Vector bundles
Vector bundles
Vector bundle orientations
The Thom isomorphism theorem
Gysin sequence
Manifolds and Poincare duality
Compactly supported cohomology
Orientation of manifolds
Poincare duality
Applications
Intersection product
The diagonal
Lefschetz fixed point theorem
Index