Mathematics 622: Algebraic Topology.

Spring 2011, 3 credits

Instructor:

Professor Stephen J. Willson
Office: Carver 411
Telephone: 294-7671
E-mail: swillson@iastate.edu
FAX: (515)-294-5454

Topology is the study of geometric shapes that seeks to describe the gross structure--holes, pieces, etc.--that would not change if the shapes were deformed. Algebraic topology makes use of algebra--principally groups (especially abelian groups) and rings---to describe features of these shapes. Examples might include distinguishing the type of hole in the middle of a spherical balloon from the type of hole in a doughnut. Many interesting examples require higher dimensions to describe--for example, Klein bottles, projective planes, and higher dimensional spheres. One famous theorem is the Brouwer Fixed Point Theorem, which asserts that any continuous map from the n-dimensional disk to itself necessarily has a fixed point. Another is that there is no homeomorphism between Euclidean spaces of different dimensions.

Prerequisites:

Math 504. Good knowledge of Math 301 is probably also sufficient.

Catalog description:

Foundations of algebraic topology. The fundamental group, simplicial homology groups, and singular homology groups.

Textbook:

A Basic Course in Algebraic Topology by William S. Massey, published by Springer-Verlag.

Likely order of topics:

Homework:

There will be weekly graded homework sets. Current homework assignments are available by clicking here.

Current course grades

Current course grades and all recorded scores are available on the web by clicking grades. Scores are listed by the first 6 digits of the second part of the student identification number. If a score has been incorrectly recorded, you should contact the instructor.

Office hours:

Tentatively MWThF 1:10 - 2:00 and Tuesday 2:10 - 3:00 in 411 Carver.
Please also feel free to make an appointment if the office hours are inconvenient for you.

Class meetings:

TuTh at 11:00-12:20 in Carver 290.

The first class is Tuesday, January 11, 2011, and the last class is Thursday, April 28, 2011. There are no classes during Spring Break (the week of March 14-18). The last day to drop without extenuating circumstances is March 25, 2011.

Grading:

Grades will be based on points accumulated. Points will be awarded for

Drop Deadline:

The last day to drop this course is March 25, 2011.

Disabilities:

Please address any special needs or special accommodations with me at the beginning of the semester or as soon as you become aware of your needs. Those seeking accommodations based on disabilities should obtain a Student Academic Accommodation Request (SAAR) form from the Disability Resources (DR) office (515-294-6624). DR is located on the main floor of the Student Services Building, Room 1076.

Information about the instructor:

For more information about the instructor, click here.

Last updated December 6, 2010.