MATH 543 Low Dimensional Topology Spring 2019
webpage:http://metu.edu.tr/~beyaz/543low/ Last updated April 18, 2019
Schedule:
1-Intersection forms
2-Topological classification of 4-manifolds
3-Smooth 4-manifolds
4-Complex surfaces
5-Symplectic 4-manifolds
6-Seiberg-Witten invariants
7-Rational blowdown and elliptic surfaces
8-Surgeries and exotic structures
9-Embedded surfaces and minimal genus
10-Branched covers
11-Resolution of singularities
Sources:
R. Gompf and A. Stipsicz, 4-Manifolds and Kirby calculus
A. Scorpan, The wild world of 4-manifolds
Other Sources:
Fintushel, R., Stern, R. J. (2009). Six lectures on four 4-manifolds. Low Dimensional Topology, IAS/Park City Math. Ser., 15.
Kirby, R. C. (1989). The topology of 4-manifolds. New York NY: Springer Verlag.
Akbulut S., 4-Manifolds, Oxford University Press 2016
Barth, W., Hulek K., Peters, C., Van De Ven, A. (2004). Compact complex surfaces 2nd Edition.
Freedman, M. H., Quinn, F. (1990). Topology of 4-manifolds. Princeton, NJ: Princeton University Press.
Fintushel, R., Stern, R. J. (1997). Rational blowdowns of smooth 4-manifolds. J. Differential Geom, 46(2), 181--235.
Fintushel, R., Stern, R. J. (1998). Knots, links, and 4-manifolds. Inventiones Mathematicae, 134(2), 363--400
Supplementary Reading:
V. A. Vassiliev, Introduction to topology. Translated from the 1997 Russian original
Allen Hatcher, Algebraic topology
Yukio Matsumoto, An introduction to Morse theory
Milnor and Stasheff, Characteristic classes
Catalog Description:
4-manifolds, surfaces in 4-manifolds, complex surfaces, complex curves and their desingularizations. Elliptic surfaces; classification of complex surfaces and logarithmic transform. Handle decomposition, Heegard splitting and Kirby diagrams. Linking numbers and framings. Kirby calculus, handle moves and Dehn surgery. Spin structures, plumbings, and related constructions. Embedded surfaces and branched covers.
Lecture Time and Place:
Tuesday 13:40-15:30 M215
Thursday 13:40-14:30 M215