Algebraic Topology

12 units · Graduate

Intermittent: 12 units Topology is a less rigid variant of geometry that studies shapes of spaces. Algebraic topology associates algebraic invariants, such as groups or rings, to such spaces. This is achieved by building a space from simpler ones or by algebraically keeping track of how to map a simple space into a given space. This course will cover the fundamental group and covering spaces, homology theories, and the cohomology ring of a space (time permitting). (Three 50 minute lectures) Prerequisites: 21-651 Min. grade B and ( 21-355 Min. grade B or 21-235 Min. grade B or 21-455 Min. grade B) and ( 21-373 Min. grade B or 21-237 Min. grade B)