| Call number: | 10123 | |
| Room/Time: | Tu, Th 2:40pm-3:55pm, 407 Math | |
| Discussions: | 5:30-7pm in room 622 | |
| TA: | Krzysztof Putyra, putyra@math.columbia.edu | |
| TA office hours: | Monday 1-4pm in Math 406 (Help room) | |
| Instructor: | Mikhail Khovanov | |
| Office: | 620 Math | |
| Office Hours: | Tuesday 4-5pm, Thursday 10:30-11:30am or by appointment | |
| E-mail: | khovanov@math.columbia.edu | |
| Midterm: | Thursday, March 14 | |
| Final exam: | Take-home | |
| Webpage: | www.math.columbia.edu/~khovanov/algtop2013 | |
We will be using the following two textbooks:
1) Homotopic topology, by A.Fomenko, D.Fuchs, and V.Gutenmacher.
Chapters 1 and 2: Homotopy and Homology,
Chapter 3: Spectral sequences,
Chapter 4: Cohomology operations,
Chapter 5: The Adams spectral sequence,
Index.
2) Algebraic
Topology by Alan Hatcher, Cambridge U Press.
Free download; printed version can be bought cheaply online.
Homotopy and homotopy equivalence. CW complexes. Cellular approximation.
Category theory, functors and adjointness.
Fundamental group and its computation. Coverings and their classification.
Fibrations and Serre fibrations. Relative homotopy groups.
Complexes and exact sequences. Homotopy sequence of a fibration.
Homotopy groups of CW complexes.
Weak equivalence and cellular approximation. Eilenberg-Maclane spaces.
Homology theory:
Chain complexes and chain maps. Homology of complexes.
Singular homology, homology of CW comlexes, computations.
Homotopy and homology, Hurewicz theorem.
Cohomology groups. Homology and cohomology with coefficients.
Kunneth formula. Multiplications in cohomology.
Applications of homology and cohomology.
Manifolds, Poincare duality.
Discussions