Instructor Prof. Sergey Finashin

1. Knots: isomorphism types and knot diagrams, operations, Wirtinger presentation of a knot group, cobordism
    Knot invariants: unknotting number, crossing number, genus and 4-genus, Seifert form, Arf invariant,
    higher signatures, Alexander and Convey polynomial, skein relations, finite type invariants and chord diagrams
2. Braids: group presentation, closed braids, calculation of Seifert forms, monodromy of algebraic curves
3. Surfaces: Dehn twists, mapping class groups, transvections
4. 3-manifolds: Heegaard splitting, surgery presentation, homology spheres, Casson invariant, open books
5. 4-manifolds: Quadratic forms, 11/8-conjecture, Spin 4-manifolds, realization of fomology classed by surfaces, Rokhlin's signature congruence, Kirby calculus, Lefschetz fibrations, Complex surfaces, Hodge diamond, the Euler characteristic and the signature of branched coverings, characteristic classes c_1, c_2, w_1, w_2 and p_1, symplectic manifolds and almost
complex structures.
 

Midterm II     dvi    ps-zipped   pdf-zipped