ELEMENTARY GEOMETRIC AND ALGEBRAIC TOPOLOGY

MATH 552

Course Description

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.

Prerequisties

(MATH 551 and MATH 541 ) or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

Satisfies

This course does not satisfy any prerequisites.

Credits

Not Reported

Offered

Not Reported

Grade Point Average

3.33

-6.49% from Historical

Completion Rate

93.33%

-2.46% from Historical

A Rate

60%

-13% from Historical

Class Size

29.31% from Historical

Instructors (2025 Fall)

Sorted by ratings from Rate My Professors

Similar Courses

ALGEBRAIC TOPOLOGY I

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.

TOPICS IN ALGEBRAIC TOPOLOGY

MATH 853

Topics in Algebraic Topology.

INTRODUCTORY TOPOLOGY I

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.

TOPICS IN GEOMETRIC TOPOLOGY

MATH 851

Advanced Topics in Geometric Topology.

SEMINAR IN TOPOLOGY

MATH 951

Selected topics in Topology.