Math 5043 Algebraic Topology Spring 2009

Time: TT, 1-2:30.
Classroom: 113 Cupples I.

There will be two text books used for the course. Several topics will come from the Math 5041 Fall 2008 text "Introduction to Smooth Manifolds", by John M. Lee, Springer Graduate Texts in Mathematics 218.
Remaining topics will come from the text "Algebraic Topology" by Allen Hatcher, Cambridge University Press. This book is available in paperback. An electronic version is available online at Hatcher

The course will attempt to cover the topics in the Course Listings description. I recommend that you read Chapter 0 of Hatcher as an introduction to algebraic topology.
Here is a tentative schedule:

• 3 Lectures: Lee, Chapter 17, first five sections. Integral curves and Flows.
• 1 Lecture: Lee, Chapter 20, first two sections. One-parameter subgroups.
• 2 Lectures: Lee, Chapter 19, first three sections. Distributions and Foliations.
• 1 Lecture: Cartan-Darboux Theorem (notes).
• 9 Lectures: Hatcher, Chapter 1. Fundamental group.
• 1 Lecture: Discrete group actions.
• 3 Lectures: Lee, Chapter 15. De Rham cohomology.
• 7 Lectures: Hatcher, Chapter 2, some of Chapter 3. Homology.

There will be a midterm examination tentatively scheduled for Thursday March 5.

The final examination is TBA.

A written homework assignment will be due at the start of class every Tuesday.

For students registered in the course, there will be detailed lesson schedule available through telesis. Homework assignments are posted there, on the calendar, as pdf files.

Qualifying Exam Study Guides:

• Fall 2008 Math 5041 Final Exam
• Spring 2005 Math 441 part of Qualifying Exam
• Fall 2004 441 Final Exam
• Fall 2003 441 Final Exam
• Spring 2004 Geometry Qual
• Fall 1992 441 Final Exam
• Spring 1993 Geometry Qual

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Gary Jensen

Last modified: Sun Apr 26 14:11:58 CDT 2009