Time and Location
M,W,F | Period 6 (12:50 PM – 1:40 PM), Little Hall 221
Description
This course is an introduction to algebraic topology. We will study the fundamental group, covering spaces, elementary homotopy theory, cofibrations and fibrations, homotopy groups, cell complexes, singular homology, and axiomatic homology. Some of the main tools include the Seifert-Van Kampen Theorem, excision, and the Mayer-Vietoris sequence.
This course will be continued next semester in MTG 6347, Topology 2, where I will cover cohomology and persistent homology.
Course Syllabus
Textbook
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Tammo tom Dieck. Algebraic Topology. European Mathematical Society, 2008. ISBN 978-3037190487.
Prerequisite
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MTG 4303/5317 or equivalent, or permission from instructor.
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Students should be able to read and understand most of the background material in Sections 1.1-1.4 and 2.1-2.4 in the course textbook.
Additional resources
There are several good alternative textbooks that could be used for parts this course.
- Allen Hatcher. Algebraic Topology. Cambridge University Press, 2002. ISBN 0-521-79540-0.
- Glen E. Bredon. Topology and Geometry. Springer, 1993. ISBN 0-387-97926-3.
- Anatoly Fomenko and Dmitry Fuchs. Homotopical Topology, 2nd edn. Springer, 2016. ISBN 978-3-319-23487-8.
- James R. Munkres. Elements of Algebraic Topology. Perseus Publishing, 1984. ISBN0-201-62728-0.
Some of the following interactive visualizations apply to this course.