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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm216-2-3,
author = {Yoshihiro Hirato and Masamichi Takase},
title = {Compositions of equi-dimensional fold maps},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {119-128},
zbl = {1244.57053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm216-2-3}
}
Yoshihiro Hirato; Masamichi Takase. Compositions of equi-dimensional fold maps. Fundamenta Mathematicae, Tome 219 (2012) pp. 119-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm216-2-3/