profhugodegaris

Species Dominance, Artilects, Artilect War, Cosmists, Terrans, Gigadeath, Essays, Media, etc

ALGEBRAIC TOPOLOGY (M1, Fulton)

Lecture Topic : ALGEBRAIC TOPOLOGY (M1, Fulton)

Recommended Text(s) :

“Algebraic Topology : A First Course”, Graduate Texts in Mathematics No. 153, William Fulton, Springer, 1995.

Approx price new on Amazon.com (hard copy) : $25

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

Lectures and Links :

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Lecture 1  (link)

Ch.1   Path Integrals

Ch.2   Angles and Deformations

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Lecture 2  (link)

Ch.3   The Winding Number

Ch.4   Applications of Winding Numbers

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Lecture 3  (link)

Ch.5   de Rham Cohomology and the Jordan Curve Theorem

Ch.6   Homology

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Lecture 4  (link)

Ch.7   Indices of Vector Fields

Ch.8   Vector Fields on Surfaces

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Lecture 5   (link)

Ch.9     Holes and Integrals

Ch.10   Mayer-Vietoris

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Lecture 6   (link)

Ch.11   Covering Spaces

Ch.12   The Fundamental Group

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Lecture 7   (link)

Ch.13   The Fundamental Group and Covering Spaces

Ch.14   The van Kampen Theorem

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Lecture 8  (link)

Ch.15   Cohomology

Ch.16   Variations

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Lecture 9  (link)

Ch.17   The Topology of Surfaces

Ch.18   Cohomology on Surfaces

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Lecture 10  (link)

Ch.19   Riemann Surfaces

Ch.20   Riemann Surfaces and Algebraic Curves

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Lecture 11  (link)

Ch.21   The Riemann-Roch Theorem

Ch.22   Toward Higher Dimensions

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Lecture 12   (link)

Ch.23   Higher Homology

Ch.24   Duality

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Lecture 13   (link)

Appendix A :   Point Set Topology

Appendix B :   Analysis

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Lecture 14   (link)

Appendix C :   Algebra

Appendix D :   On Surfaces

Appendix E :   Proof of Borsuk’s Theorem

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