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ALGEBRAIC TOPOLOGY (M2, May)

Lecture Topic : ALGEBRAIC TOPOLOGY (M2, May)

Prerequisites : Algebraic Topology (M1);

Recommended Text(s) :

“A Concise Course in Algebraic Topology”, J.P. May,UniversityofChicagoPress, 1999.

Approx price new on Amazon.com (hard copy) : $24

Approx price second hand on Amazon.com (hard copy) : $20

Availability free on eMule.com (e-format) : Yes

eMule search key word(s) : May, Algebraic Topology

Lectures and Links :

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Lecture 1  (link)

Ch.1   The Fundamental Group and Some of its Applications

Ch.2   Categorical Language and the van Kampen Theorem

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Lecture 2  (link)

Ch.3   Covering Spaces

Ch.4   Graphs

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Lecture 3  (link)

Ch.5   Compactly Generated Spaces

Ch.6   Cofibrations

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Lecture 4  (link)

Ch.7   Fibrations

Ch.8   Based Cofiber and Fiber Sequences

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Lecture 5   (link)

Ch.9     Higher Homotopy Groups

Ch.10   CW-Complexes

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Lecture 6   (link)

Ch.11   The Homotopy Excision and Suspension Theorems

Ch.12   A Little Homological Algebra

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Lecture 7   (link)

Ch.13   Axiomatic and Cellular Homology Theory

Ch.14   Derivations of Properties from the Axioms

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Lecture 8  (link)

Ch.15   The Hurewicz and Uniqueness Theorems

Ch.16   Singular Homology Theory

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Lecture 9  (link)

Ch.17   Some More Homological Algebra

Ch.18   Axiomatic and Cellular Cohomology Theory

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Lecture 10  (link)

Ch.19   Derivations of Properties from the Axioms

Ch.20   The Poincare Duality Theorem

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Lecture 11  (link)

Ch.21   The Index of Manifolds; Manifolds with Boundary

Ch.22   Homology, Cohomology, and K(p,n)s

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Lecture 12   (link)

Ch.23   Characteristic Classes of Vector Bundles

Ch.24   An Introduction to K-Theory

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Lecture 13   (link)

Ch.25   An Introduction to Cobordism

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