MAT 542/540: Algebraic Topology
Stony Brook            Fall 2016 |
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Here is general information about the course. The MW lectures by Aleksey will take place 2:30-3:50pm in Physics P-128. The Friday discussions with Dennis/Chandrika will be held 12:30-2:30 in Math 5-127.
The second paragraph of this gives a quick definition of pseudocycle. It is then shown that the group of pseudocycle equivalences and the Z homology are isomorphic as graded abelian groups. Two natural questions arise.
Name:
Aleksey Zinger    
E-mail: azinger@math
    Office: Math Tower 3-111
Office Hours: Tu 9-10 in Math P-143, 10-12 in Math 3-111 (or catch me at tea)
Name:
Dennis Sullivan    
E-mail: dennis@math
   
Office: Math Tower 5-114
Office Hours: upon request or random encounter
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Date | Topic | Read | Suggested Problems |
08/29, M | Simplicial complexes | Sections 1-4 | HW1 note |
08/31, W | CW complexes and homology | Section 38 | |
09/02, F | Discussion with Dennis/Chandrika | from Dennis | |
09/05, M | Labor Day | ||
09/07, W | Simplicial homology | Sections 5,7,10 | HW2 |
09/09, F | Discussion with Dennis/Chandrika | from Dennis | |
09/12, M | Homology of surfaces and cones | Sections 6,8 | HW3 |
09/14, W | Relative homology, Mayer-Vietoris | Sections 9,23-25 | |
09/16, F | Discussion with Dennis/Chandrika | ||
09/19, M | Homology pushforwards I | Sections 12,13,11 | HW4 |
09/21, W | Chain equivalences | Sections 13,46 | |
09/23, F | Discussion with Dennis/Chandrika | ||
09/26, M | Simplicial subdivisions | Sections 46,15,17 | HW5 |
09/28, W | Topological invariance | Sections 17,18 | |
09/30, F | Discussion with Dennis/Chandrika | ||
10/03, M | Homology pushforwards II | Sections 18,14 | HW6 |
10/05, W | Simplicial approximations | Sections 16,19,20 | |
10/07, F | Discussion with Dennis/Chandrika | ||
10/10, M | Applications and generalities | Sections 21,22,26-28 | HW7 |
10/12, W | Singular homology | Sections 29,30 | |
10/14, F | Discussion with Dennis/Chandrika | ||
10/17, M | Mayer-Vietoris and Excision | Sections 31-33 | HW8 |
10/19, W | Singular vs. simplicial homology | Section 34 | |
10/21, F | Discussion with Dennis/Chandrika | ||
10/24, M | Singular vs. CW homology | Sections 37-40 | HW9 |
10/26, W | Invariance of domain | Section 36 | |
10/28, F | Discussion with Dennis/Chandrika | ||
10/31, M | Cohomology of chain complexes | Sections 41,45,46 | HW10 |
11/02, W | Cohomology of topological spaces | Sections 44,42,43 | |
11/04, F | Discussion with Dennis/Chandrika | ||
11/07, M | Cohomology theory | Sections 44,47,48 | HW11 |
11/09, W | Cup and cap products | Sections 66,50,51,57 | |
11/11, F | Discussion with Dennis/Chandrika | ||
11/14, M | Kunneth formula for homology | Sections 54,58,55 | HW12 |
11/16, W | Kunneth formula for cohomology | Sections 59,60 | |
11/18, F | Discussion with Dennis/Chandrika | ||
11/21, M | Homological algebra wrapup | Sections 61,52,53 | HW13 |
11/23, W | Thanksgiving Break | ||
11/25, F | |||
11/28, M | Fundamental class of oriented manifold | MS pp270-275 | HW14 |
11/30, W | Poincare Duality for oriented manifolds | MS pp276-279 | |
12/02, F | Discussion with Dennis/Chandrika | ||
12/05, M | Some applications | Section 65,68 | HW15 |
12/07, W | Computations on manifolds: an overview | MS Sections 9-11 | |
12/09, F | Discussion with Dennis/Chandrika |
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