MTH 3107 - Topology II

Winter 1998

Course Information

Course: MTH 3107  (Topology II)
Instructor: Alex Suciu
Time and Place: Mon. & Wed. at 7:15 - 8:45 PM, in 544 NI
Office Hours: By appointment
Prerequisites: MTH 3105  (Topology I)
Textbook: Topology and Geometry, by Glen Bredon, Springer-Verlag, GTM #139

Course Description

This course is an introduction to homology theory. We will start with singular homology theory: axioms, homological algebra, homology with coefficients, Mayer-Vietoris sequence, degrees of maps, Euler characteristic. Next, we will introduce CW-complexes and study cellular homology. We will illustrate these techniques by many geometrical examples (surfaces, projective spaces, grassmanians, lens spaces, products, etc), and derive various applications (Jordan Curve Theorem, Borsuk-Ulam Theorem, Brouwer and Lefschetz-Hopf Fixed Point Theorems, etc). Time permitting, we will touch upon cohomology theory and duality on compact manifolds.

The grade for the course will be based on problem sets and a final exam. 

Here are some qualifying exams in Topology, based in part on the material covered in this course.

Final Exam

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Department of Mathematics  Office:  441 Lake Hall 
Northeastern University Phone:  (617) 373-4456 
Boston, MA, 02115  Email: alexsuciu@neu.edu 
Home Created: December 27, 1997.   Last modified: March 21, 1998.
URL:  http://www.math.neu.edu/~suciu/mth3107/top2.w98.html