MATH 422
Algebraic Topology Fall 2019
Division III Quantative/Formal Reasoning

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Is a sphere really different from a torus? Can a sphere be continuously deformed to a point? Algebraic Topology concerns itself with the classification and study of topological spaces via algebraic methods. The key question is this: How do we really know when two spaces are different and in what senses can we claim they are the same? Our answer will use several algebraic tools such as groups and their normal subgroups. In this course we will develop several notions of “equality” starting with the existence of homeomorphisms between spaces. We will then explore several weakenings of this notion, such as homotopy equivalence, having isomorphic homology or fundamental groups, and having homeomorphic universal covers.
The Class: Type: lecture
Limit: 30
Expected: 15
Class#: 1590
Grading: no pass/fail option, no fifth course option
Requirements/Evaluation: evaluation will be based primarily on homework and exams
Prerequisites: MATH 355 or permission of instructor
Enrollment Preferences: Math majors primarily, and Juniors and Seniors secondarily
Distributions: Division III Quantative/Formal Reasoning

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