Elective List

Topology of space of continuous mappings. Homotopy. Extension. Retraction and deformation. Algebraization of topological problems. Homotopy groups. Fundamental group. Computations of the fundamental and homotopy groups of closed surfaces, topological invariance of the Euler characteristics. Homology groups of simplicial complexes and polyhedra. Barycentric subdivision, simplicial mappings. Singular homology. Homology groups of spheres, cell complexes and projective spaces. Degree of a mapping. Lefschetz number of simplicial and continuous mappings.