Topology

(3 Credit Hours) · Undergraduate

Topology is concerned with the question of whether one geometric object can be continuously deformed into another. The course will introduce some of the basic objects of study in topology: knots and surfaces. A knot is an entangled circle in 3-dimensional space. A surface is the boundary of a solid, smooth object in space, such as a basketball, a pretzel or a mug. Given two knots, can one of them be continuously transformed into the other? Or, can the boundary of a ball gradually be turned into the boundary of a pair of scissors? We will study these topological objects and develop techniques to distinguish and classify them.