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ma3403:2019h:start [2019-11-05]
runegha [Lecture Plan] 		ma3403:2019h:start [2019-11-10]
runegha [Lecture Plan]
Linje 42: Linje 42:
 |  1.1  |  21/08  | Review of topological spaces, homotopies  |  1.1-1.5  | [Q], lect. 2  | |  1.1  |  21/08  | Review of topological spaces, homotopies  |  1.1-1.5  | [Q], lect. 2  |
 |  1.2  |  22/08  | Definition of singular homology           |  2.1-2.5  | [Q], lect. 3  | |  1.2  |  22/08  | Definition of singular homology           |  2.1-2.5  | [Q], lect. 3  |
-|  2.1  |  28/08  | H<sub>0</sub>, disjoint unions, orientations, functoriality  | 2.6-2.9 | [Q], lect. 4  |+|  2.1  |  28/08  | H<sub>0</sub>, disjoint unions, orientations, functoriality  |  2.6-2.9  | [Q], lect. 4  |
 |  2.2  |  29/08  | Δ-complexes, simplicial homology  |  3.1-3.3  | [H], p. 102-107  | |  2.2  |  29/08  | Δ-complexes, simplicial homology  |  3.1-3.3  | [H], p. 102-107  |
-|  3.1  |  04/09  | Relative homology, exact sequences, singular and simplicial homology  | 4.1-4.3 | [Q], lect. 5, [H], p.138-130 | +|  3.1  |  04/09  | Relative homology, exact sequences, singular and simplicial homology  |  4.1-4.3  | [Q], lect. 5, [H], p.138-130 | 
-|  3.2  |  05/09  | Eilenberg-Steenrod axioms/excision, exercises week 1 | 4.4-4.5 | [Q], lect. 6 |+|  3.2  |  05/09  | Eilenberg-Steenrod axioms/excision, exercises week 1 |  4.4-4.5  | [Q], lect. 6 |
 |  4.1  |  11/09  | Homology of spheres, applications |  4.6-4.8  | [Q], lect. 6,7 | |  4.1  |  11/09  | Homology of spheres, applications |  4.6-4.8  | [Q], lect. 6,7 |
 |  4.2  |  12/09  | Mayer-Vietoris, exercises 2 |  4.9  | [G], lect. I.6 | |  4.2  |  12/09  | Mayer-Vietoris, exercises 2 |  4.9  | [G], lect. I.6 |
 |  5.1  |  18/09  | Cell complexes  |  5.1-5.3  | [Q], lect. 13,14 | |  5.1  |  18/09  | Cell complexes  |  5.1-5.3  | [Q], lect. 13,14 |
 |  5.2  |  19/09  | Cellular homology, exercise 3 |  5.4-5.5  | [Q], lect. 14,15 | |  5.2  |  19/09  | Cellular homology, exercise 3 |  5.4-5.5  | [Q], lect. 14,15 |
-|  6.1  |  25/09  | Degrees, homology of real projective space  | 5.6-5.7 | [Q], lect. 7,15  | +|  6.1  |  25/09  | Degrees, homology of real projective space  |  5.6-5.7  | [Q], lect. 7,15  | 
-|  6.2  |  26/09  | Exterior product, homotopy invariance, exercises 4  | 6.1-6.3 | [Q], lect. 10,11, [G], lect. I.5  | +|  6.2  |  26/09  | Exterior product, homotopy invariance, exercises 4  |  6.1-6.3  | [Q], lect. 10,11, [G], lect. I.5  | 
-|  7.1  |  02/10  | Excision, locality, barycentric subdivision  | 6.4-6.5 | [Q], lect. 12, [G], lect. I.7  |+|  7.1  |  02/10  | Excision, locality, barycentric subdivision  |  6.4-6.5  | [Q], lect. 12, [G], lect. I.7  |
 |  7.2  |  03/10  | Tensor products, exercises 5  |  7.1  | [Q], lect. 17  | |  7.2  |  03/10  | Tensor products, exercises 5  |  7.1  | [Q], lect. 17  |
 |  8.1  |  09/10  | Homology with coefficients  |  7.2-7.3  | [Q], lect. 16,17  | |  8.1  |  09/10  | Homology with coefficients  |  7.2-7.3  | [Q], lect. 16,17  |
Linje 63: Linje 63:
 |  11.2  |  31/10  | Ring structures on cochains and cohomology, exercises 9  |  10.2-10.3  | [G], lect. II.6  | |  11.2  |  31/10  | Ring structures on cochains and cohomology, exercises 9  |  10.2-10.3  | [G], lect. II.6  |
 |  12.1  |  06/11  | Cohomology rings of projective spaces  |  10.4  | [H], p. 212-214  | |  12.1  |  06/11  | Cohomology rings of projective spaces  |  10.4  | [H], p. 212-214  |
 +|  12.2  |  07/11  | Manifolds, exercises 10  |  11.1  | [H], p. 230-239  |
 +|  13.1  |  13/11  | Orientations, fundamental classes, cap products and Poincaré duality  |  11.2-3  | [H], p. 233-241  |
 +|  13.2  |  14/11  | Poincaré duality and cup products, exercises 11   |  11.4  | [H], p. 249-250  |
 +|  14.1  |  20/11  | Cohomology with compact support, proof of Poincaré duality (*) |  11.5-6  | [H], p. 242-248  |
 +|  14.2  |  21/11  | Review  |  |  |
 +
 +
 +(*) Not examinable
 ===== Course material ===== ===== Course material =====
  
2019-11-15, Rune Gjøringbø Haugseng