Math 6620 -- Algebraic Topology -- W. Cherry

Class Meets:   MWF 11-11:50 in GAB 461.
Final Exam:   10:30-12:30 Monday, December 11 in GAB 461.

Instructor: William Cherry

Office Location:General Academic Building (GAB) 405. 
Office Hours: Mondays 12:30-1:30
Tuesdays & Thursdays 1:00-3:00
Wednesdays 9:30-10:30, 12:30-1:30, and 4-5
and by appointment.


Glen Bredon, Topology and Geometry, Springer, 1993.

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Course Hand-Outs

Course syllabus

Optional Homework

Date AssignedDue not later than Assignment details
Aug 28Sep 11I.2#2, I.3#1 and 6, I.4, #1 and 5. Also if A is a subset of a topological space X, is the subspace toplogy on A the largest topology on A such that the inclusion map is continuous? The smallest? Neither one?
Sep 6Sep 20I.13#3-7. Also, if you have some familiarity with complex numbers, check that CP1 is homeomorphic to S2.
Sep 11Sep 20I.14#1, 3, 4, 6, 9.

Lecture Summaries

Review of and Crash Course in General Topology
Aug 28Topological Vocabulary: Ch. I, Sections 2-3
Aug 30Mostly connectedness: Ch. I, Section 4; plus definition of Hausdorff: Ch. I, Section 5
Sep 1Compactness, proper mappings, product topology: Ch. I, Sections 7-8
Sep 6Quotient topology: Ch. I, Section 13
Sep 8Homotopy: Ch. I, Section 14
Sep 11More Homotopy: Ch. I, Section 14
A brief tour of differentiable manifolds: This material provides motivation and examples for what we will be studying. For those interested, an undergraduate level treatment can be found in Guillemin and Pollack, Differential Topology, which is inspired by the well-known introduction by Milnor, Topology from the Differentiable Viewpoint.
Sep 13Definitions of (smooth) manifold and examples: Ch. II, Sections 2-4
Sep 15Poincare Conjecture, Exotic Spheres, the graph of the absolute value function in R2 as a manifold (compare with the discussion of the cone following Definition II.4.5), manifold with boundary (Definition II.2.7), brief discussion without proof of classification of one and two dimensional compact connected manifolds, allowing boundary in the 1-dimensional case, tangent vectors & differentials (Ch. II, Sec. 5), Tangent Bundles (Ch. II, Sec. 9), and the Whitney Embedding Theorem without proof (Ch. II, Sec. 10)

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