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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 (hard copy) : $24

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

Availability free on (e-format) : Yes

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

Lectures and Links :


Lecture 1  (link)

Ch.1   The Fundamental Group and Some of its Applications

Ch.2   Categorical Language and the van Kampen Theorem


Lecture 2  (link)

Ch.3   Covering Spaces

Ch.4   Graphs


Lecture 3  (link)

Ch.5   Compactly Generated Spaces

Ch.6   Cofibrations


Lecture 4  (link)

Ch.7   Fibrations

Ch.8   Based Cofiber and Fiber Sequences


Lecture 5   (link)

Ch.9     Higher Homotopy Groups

Ch.10   CW-Complexes


Lecture 6   (link)

Ch.11   The Homotopy Excision and Suspension Theorems

Ch.12   A Little Homological Algebra


Lecture 7   (link)

Ch.13   Axiomatic and Cellular Homology Theory

Ch.14   Derivations of Properties from the Axioms


Lecture 8  (link)

Ch.15   The Hurewicz and Uniqueness Theorems

Ch.16   Singular Homology Theory


Lecture 9  (link)

Ch.17   Some More Homological Algebra

Ch.18   Axiomatic and Cellular Cohomology Theory


Lecture 10  (link)

Ch.19   Derivations of Properties from the Axioms

Ch.20   The Poincare Duality Theorem


Lecture 11  (link)

Ch.21   The Index of Manifolds; Manifolds with Boundary

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


Lecture 12   (link)

Ch.23   Characteristic Classes of Vector Bundles

Ch.24   An Introduction to K-Theory


Lecture 13   (link)

Ch.25   An Introduction to Cobordism



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