Office: AB 615, tel 784 6020, fax 784 6378, email naik
Office Hours: TR 2:30-4, and by appointment
Course Prerequisites: MATH 440 (Point-Set Topology), MATH 331 (Abstract Algebra)
Course webpage: http://unr.edu/homepage/naik/classes/774/
Text book: Lecture notes will be handed out in class. For a preliminary
For an older set of knots, click
Course grades: Grades will be based on homework and a take-home final project.
There will be no in-class exams.
A knot is an embedding of a circle in the three-dimensional space. We will begin the course with the definition of a knot and study several examples from the perspective of an equivalence relation called knot concordance. The equivalence classes form a group under an operation of joining two knots together called connect sum. This is an abelian group the structure of which is not well-understood. There are several open problems in this area which are easy to state. We will study knot invariants which help us understand the group and tools which help tackle special cases of open problems.
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