Low Dimensional Topology

Course content

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.