ELEMENTARY GEOMETRIC AND ALGEBRAIC TOPOLOGY

MATH 751

An introduction to algebraic and differential topology. Elements of homotopy theory, fundamental group, covering spaces. Differentiable manifolds, tangent vectors, regular values, transversality, examples of compact Lie groups. Homological algebra, chain complexes, cell complexes, singular and cellular homology, calculations for surfaces, spheres, projective spaces, etc. Familiarity with undergraduate algebra and topologyMATH 541or551) is strongly recommended.

MATH 853

Topics in Algebraic Topology.

MATH 951

Selected topics in Topology.

MATH 851

Advanced Topics in Geometric Topology.

MATH 753

Higher homotopy groups, elements of obstruction theory, fibrations, bundle theory, classifying spaces, applications to smooth mainfolds, differential forms, vector bundles, characteristic classes, cobordism, applications and calculations. Basic graduate topology courses (e.g.MATH 751and752) are strongly recommended.