Topic: The Fundamental Group of the Circle and Applications

Exponential Covering Map and Its Deck Transformations

Evenly Covered Arcs and Local Lifting

Dominance Estimates for Polynomials on Large Circles

Diagnosing Lift, Orientation, and Extension Errors

Degree of a Normalized Polynomial on the Boundary

Degrees of Power Maps, Reflections, and Compositions

Degree of a Circle Map from Its Lift

Computing the Fundamental Group of the Circle

Brouwer Fixed Point Theorem for the Disk

Building a Boundary Retraction from a Fixed-Point-Free Map