Course: | MTH 3105, Topology I |
Instructor: | Alex Suciu |
Time and Place: | Tue. & Th. at 5:30 - 7:00 PM, in 509 LA |
Office Hours: | Mon., Tue. & Th. at 3:00 - 4:00, in 441 LA |
Prerequisites: | MTH 3010, Basics of Analysis |
Textbook: | An Introduction to Topology and Homotopy, by Allan Sieradski, PWS-Kent, Boston, 1992 |
This course provides an introduction to Topology, requiring only some elementary backround in Analysis.
The first (shorter) part of the course treats General Topology. The objects of study are metric and topological spaces. The properties that are studied include connectedness, compactness, completeness and separation. We also introduce several constructions of spaces, and study the invariance of various properties under topological equivalence.
The second part of the course treats the basics of Homotopy Theory. It starts with the fundamental group of a space, and methods to compute it (the Seifert-Van Kampen theorem). It proceeds with a study of the homotopy category, including fibrations and cofribations, adjunction spaces, and homotopy equivalences. The culmination of this course is the study of covering spaces, and their relationship with fundamental groups. The course ends with the classification of 2-dimensional surfaces, and the study of their covering spaces.
Time permitting, other topics will be touched upon, e.g., cell complexes and their fundamental groups and coverings, vector fields and the Poincaré-Hopf index theorem, simplicial homology and Euler characteristic.
Created: October 1, 1996. Last modified: October 19, 1996.