Once upon a time there was a fixed point…. (Hi havia una vegada un punt fix….) (Catalan. English summary) Zbl 1368.55002

Castellana, Natàlia

Butll. Soc. Catalana Mat. 31, No. 2, 99-120 (2016).

Summary: One of the classical results we can find in the literature on algebraic topology is Brouwer’s fixed point theorem, proved using covering spaces techniques, fundamental group calculation and homology groups.
In this paper we present a proof based on a lemma from topological combinatorics, Sperner’s lemma, which avoids the techniques mentioned-above.

MSC:

55M20

Fixed points and coincidences in algebraic topology

Keywords:

algebraic topology; combinatorics