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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 (hard copy) : $25

Approx price second hand on (hard copy) : $22

Availability free on (e-format) : Yes

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

Lectures and Links :


Lecture 1  (link)

Ch.1   Path Integrals

Ch.2   Angles and Deformations


Lecture 2  (link)

Ch.3   The Winding Number

Ch.4   Applications of Winding Numbers


Lecture 3  (link)

Ch.5   de Rham Cohomology and the Jordan Curve Theorem

Ch.6   Homology


Lecture 4  (link)

Ch.7   Indices of Vector Fields

Ch.8   Vector Fields on Surfaces


Lecture 5   (link)

Ch.9     Holes and Integrals

Ch.10   Mayer-Vietoris


Lecture 6   (link)

Ch.11   Covering Spaces

Ch.12   The Fundamental Group


Lecture 7   (link)

Ch.13   The Fundamental Group and Covering Spaces

Ch.14   The van Kampen Theorem


Lecture 8  (link)

Ch.15   Cohomology

Ch.16   Variations


Lecture 9  (link)

Ch.17   The Topology of Surfaces

Ch.18   Cohomology on Surfaces


Lecture 10  (link)

Ch.19   Riemann Surfaces

Ch.20   Riemann Surfaces and Algebraic Curves


Lecture 11  (link)

Ch.21   The Riemann-Roch Theorem

Ch.22   Toward Higher Dimensions


Lecture 12   (link)

Ch.23   Higher Homology

Ch.24   Duality


Lecture 13   (link)

Appendix A :   Point Set Topology

Appendix B :   Analysis


Lecture 14   (link)

Appendix C :   Algebra

Appendix D :   On Surfaces

Appendix E :   Proof of Borsuk’s Theorem


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