Compositions of equi-dimensional fold maps
Volume 216 / 2012
Fundamenta Mathematicae 216 (2012), 119-128
MSC: Primary 57R45; Secondary 55Q45, 57R35, 55Q35.
DOI: 10.4064/fm216-2-3
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 these operations we explicitly construct several fold maps with convenient properties, including a fold map which represents the generator of the stable $6$-stem.
