Atoms of topology. (English) Zbl 1013.55001

Baues, Hans-Joachim

Jahresber. Dtsch. Math.-Ver. 104, No. 4, 147-164 (2002).

Summary: In 1932, Alexandroff wrote the introductory essay “Einfachste Grundbegriffe der Topologie” on polyhedra and homology. Following this tradition we explain the elementary notion of an atom in topology which leads to outstanding problems of Mathematics: the computation of stable homotopy groups of spheres and the problem of representation theory. In low dimensions \(\leq 11\) we describe a complete list of such atoms.

MSC:

55-02	Research exposition (monographs, survey articles) pertaining to algebraic topology
55P15	Classification of homotopy type

Keywords:

homotopy types of finite polyhedra; suspension; atom; wild representation type; finite space; homotopy groups of spheres