Title of the course: Shapes of Surfaces
Instructor: Asst. Prof. Bahar Acu
Institution: Claremont Colleges: Pitzer College
Dates: 24-30 July 2023
Prerequisites: Multivariable Calculus, Linear Algebra
Level: Advanced undergraduate, Beginning Undergraduate
Abstract: This course is designed to be an introductory course in geometric topology. Topology is the study of properties of shapes that do not fundamentally change when they are bent and/or stretched without poking holes or ripping apart. As the famous catch sentence goes; To a topologist, a donut and a coffee cup (with a handle) are the same thing, since one can be deformed into the other “continuously”, i.e. only via bending and/or stretching. Starting from tangled loops (called knots), and then some, we will talk about surfaces and their properties, surface classification theorem, cutting and pasting of surfaces, distinguishing topological shapes via topological methods such as knot invariants and Euler characteristics. The class discussions will include use of various tactile objects to help with imagining structures of shapes.
Language: EN