| January 16: |
Introduction
Recap of general topology
Fundamental group
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| January 17: |
Brower's fixed point theorem in dimension 2
Theorem of the invariance of domain in dimension 2
Introduction to higher homotopy groups
Singular homology
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| January 23: |
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| January 24: |
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| January 30: |
Hurewicz theorem
Homology homomorphisms induced by continuous maps
Homotopy invariance of singular homology
Short and long exact sequences of chain complexes
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| January 31: |
Relative homology
Subdivision homomorphism
Theorem of small chains
Excision
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| February 6: |
Mayer-Vietoris long exact sequence
Homology of spheres
Local homology
Theorem of the invariance of domain
Brower's fixed point theorem
Topological degree
Hairy ball theorem
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| February 7: |
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| February 9: |
(exceptional session)
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| February 13: |
(canceled session)
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| February 14: |
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| February 20: |
CW complexes
CW decomposition of spheres and projective spaces
Cellular homology theorem
Homology of quotients and wedge sums
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| February 21: |
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| March 12: |
Boundary homomorphism in cellular homology
Homology of real projective spaces
Euler characteristic
Singular homology with coefficients
Singular cohomology
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| March 13: |
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| March 19: |
Properties of singular cohomology
Free resolutions
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| March 20: |
Solution of the exercise on Poincaré's hypercube manifold:
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| March 26: |
Ext and Tor functors
Proof of the universal coefficient theorem
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| March 27: |
Some solutions:
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| Avril 2: |
Cup product
Crossed cup product
Künneth theorem
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| Avril 3: |
Some solutions:
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| April 9: |
Orientability of topological manifolds
Fundamental class
Cohomology with compact support
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| April 10: |
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| April 16: |
Cap product
Poincaré duality
Proof of Poincaré duality:
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| April 17: |
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