Contents
11 The Exponential Map 2
11.1 The Exponential Map on the Complex Plane . . . . . . . . . . 2
11.2 Evenly Covered Open Sets . . . . . . . . . . . . . . . . . . . . 4
11.3 Riemann Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 6
11.4 Path Lifting and the Monodromy Theorem . . . . . . . . . . . 8
12 Winding Numbers 11
12.1 Winding Numbers of Closed Curves . . . . . . . . . . . . . . . 11
12.2 The Fundamental Theorem of Algebra . . . . . . . . . . . . . 13
12.3 The Brouwer Fixed Point Theorem . . . . . . . . . . . . . . . 14
12.4 The Borsuk-Ulam Theorem . . . . . . . . . . . . . . . . . . . 15