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HOMOLOGY-COHOMOLOGY (M2, Goldberg)

Lecture Topic : HOMOLOGY-COHOMOLOGY (M2, Goldberg)

Prerequisites : Algebraic Topology (M1); Lie Algebras (M1); Differential Manifolds (M1); Complex Manifolds (M1);

Recommended Text(s) :

“Curvature and Homology”, Revised Edition, Samuel I. Goldberg,Dover, 1998.

Approx price new on Amazon.com (hard copy) : $18

Approx price second hand on Amazon.com (hard copy) : $14

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

eMule search key word(s) : Goldberg, Curvature Homology

Lectures and Links :

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Lecture 1  (link)

Ch.1   Riemannian Manifolds

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Lecture 2  (link)

Ch.2   Topology of Differentiable Manifolds

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Lecture 3  (link)

Ch.3   Curvature and Homology of Riemannian Manifolds

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Lecture 4  (link)

Ch.4   Compact Lie Groups

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Lecture 5  (link)

Ch.5   Complex Manifolds

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Lecture 6  (link)

Ch.6   Curvature and Homology of Kaehler Manifolds

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Lecture 7  (link)

Ch.7   Groups of Transformations of Kaehler and Almost Kaehler Manifolds

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Lecture 8  (link)

Appendix A :   de Rham’s Theorems

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Lecture 9  (link)

Appendix B :   The Cup Product

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Lecture 10  (link)

Appendix C :   The Hodge Existence Theorem

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Lecture 11  (link)

Appendix D :   Partition of Unity

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Lecture 12  (link)

Appendix E :   Holomorphic Bisectional Curvature

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Lecture 13  (link)

Appendix F :   The Gauss-Bonnet Theorem

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Lecture 14  (link)

Appendix G :   Some Applications of the Generalized Gauss-Bonnet Theorem

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Lecture 15  (link)

Appendix H :   An Application of Bochner’s Lemma

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Lecture 16  (link)

Appendix I :   The Kodaira Vanishing Theorems

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Links to Other Lecturers on this Topic :

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