These notes are an expanded version of my talk at the ICRA 2018 in Prague,
Czech Republic; they are based on joint work with Tobias Dyckerhoff and Tashi
Walde. In them we relate Iyama's higher Auslander algebras of type A
to Eilenberg--Mac Lane spaces in algebraic topology and to higher-dimensional
versions of the Waldhausen S-construction from algebraic
K-theory.Comment: 16 pages. The author's contribution to the Proceedings of the ICRA
2018, v.2 minor edits following referee repor