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FIBRE BUNDLES (M2, Husemoller)

Lecture Topic : (Pure Math) FIBRE BUNDLES (M2, Husemoller)

Prerequisites : Abstract Algebra (M1); Homology-Cohomology (M1); Homotopy Theory (M1); Differential Manifolds (M1);

Recommended Text(s) :

“Fibre Bundles”, 2nd Edn., Graduate Texts in Mathematics (GTM) No. 20, Dale Husemoller, Springer, 1975.

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

Approx price second hand on Amazon.com (hard copy) : $46

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eMule search key word(s) : Husemoller, Fibre Bundles

Lectures and Links :

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Lecture 1  (link)

Ch.1   Preliminaries on Homotopy Theory

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Lecture 2  (link)

Ch.2   Generalities on Bundles

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Lecture 3  (link)

Ch.3   Vector Bundles

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Lecture 4 (link)

Ch.4   General Fibre Bundles

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Lecture 5  (link)

Ch.5   Local Coordinate Description of Fibre Bundles

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Lecture 6  (link)

Ch.6   Change of Structure Group in Fibre Bundles

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Lecture 7  (link)

Ch.7   Calculations Involving the Classical Groups

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Lecture 8  (link)

Ch.8   Stability Properties of Vector Bundles

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Lecture 9  (link)

Ch.9   Relative k-Theory

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Lecture 10  (link)

Ch.10   Bott Periodicity in the Complex Case

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Lecture 11  (link)

Ch.11   Clifford Algebras

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Lecture 12  (link)

Ch.12   TheAdamsOperations and Representations

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Lecture 13  (link)

Ch.13   Representation Rings of Classical Groups

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Lecture 14  (link)

Ch.14   The Hopf Invariant

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Lecture 15  (link)

Ch.15   Vector Fields on the Sphere and Stable Homotopy

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Lecture 16  (link)

Ch.16   Chern Classes and Stieffel-Whitney Classes

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Lecture 17  (link)

Ch.17   Differentiable Manifolds

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Lecture 18  (link)

Ch.18   General Theory of Characteristic Classes

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Lecture 19  (link)

Appendix 1 : Dold’s Theory of Local Properties of Bundles

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Lecture 20  (link)

Appendix 2 : On the Double Suspension

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