Compositions of equi-dimensional fold maps

Abstract

According to Ando’s theorem, the oriented bordism group of fold maps of n-manifolds into n-space is isomorphic to the stable n-stem. Among such fold maps we define two geometric operations corresponding to the composition and to the Toda bracket in the stable stem through Ando’s isomorphism. By using the operations we explicitly construct several fold maps with favourable properties, including a fold map which represents the generator of the stable 6-stem.