TOPICS IN ALGEBRAIC TOPOLOGY

MATH 863

Geometry of several complex variables; algebraic groups, abelian varieties; topological aspects of algebraic geometry, including sheaf theory and homology theory; advanced theory of local rings; intersection theory of algebraic varieties.

MATH 552

Introduction to algebraic topology. Emphasis on geometric aspects, including two-dimensional manifolds, the fundamental group, covering spaces, basic simplicial homology theory, the Euler-Poincare formula, and homotopy classes of mappings.

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.