MTH 3105 - Topology I

Fall 1996


Course Information

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


Course Description

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.


Department of Mathematics
Northeastern University
Boston, MA, 02115
Office: 441 LA
Phone: (617) 373-4456
Email: alexsuciu@neu.edu

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Created: October 1, 1996. Last modified: October 19, 1996.