A friendly introduction to low-dimensional topology: knots, surfaces, three-dimensional manifolds, the fundamental group, and point-set topology. Cultivate the intuitive ideas of continuity, convergence, and connectedness and get familiar with knot theory, the topology of surfaces and three-dimensional manifolds, and elementary homotopy theory.

• References: Topology Now! by Robert Messer and Philip Straffin
• Prerequisites: Students enrolled in this project should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs. Courses in multivariable calculus and linear algebra plus a proof-oriented course would satisfy this prerequisite. A semester of abstract algebra is desirable.
• Meetings: Once per week from Sept 19, 2022 to Dec 15, 2022
• Type: Reading
• Size: 1-3 students

Instructor: Alexander Voronov, Mathematics, University of Minnesota