Instructor: Dr. Boldizsár Kalmár
Text: Allan Hatcher: Algebraic Topology and class notes
basic algebra (vector spaces, groups), basic analysis (differentiable
functions, continuous functions in
Knowledge of general topology is not necessary, the algebraic topology course is independent of the introductory topology course. Topics:
This course is rather "Basic algebraic and geometric topology". The goal of the lectures is to give a wide and detailed view of the most important tools in algebraic and geometric topology. These connect the most natural "naive" and elementary geometric ideas and constructions with various fields of modern mathematics. The course is useful to students who want to have a global picture of a big part of today's mathematics or to students who are interested in mathematical research.
- Basic notions, fundamental group and its applications, surfaces.
- 3-manifolds, knots, surgeries, 4-manifolds.
- Smooth manifolds, smooth maps, analysis on manifolds, applications in algebraic topology.
- Morse functions, classification of surfaces.
- Degree of a map and its applications, maps into spheres and Hopf theorem.
- Higher homotopy groups and exact sequences.
- Homology groups, functoriality and constructions.