Algebraic Topology · Problem 2.2.1

Homology — Allen Hatcher

Mathematics — Topology · degree-theory

Problem

Prove the Brouwer fixed point theorem for maps

f: D^n \to D^n

by applying degree theory to the map

S^n \to S^n

that sends both the northern and southern hemispheres of

S^n

to the southern hemisphere via

f

. [This was Brouwer's original proof.]