Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 53, Number 2 (2001), 357-382.
Folding maps and the surgery theory on manifolds
Let be a smooth map between -dimensional oriented manifolds which has only folding singularities. Such a map is called a folding map. We prove that a folding map : canonically determines the homotopy class of a bundle map of to , where and are the trivial line bundles over and respectively. When is a closed manifold in addition, we define the set of all cobordism classes of folding maps of closed manifolds into of degree 1 under a certain cobordism equivalence. Let denote the space , where denotes the space of all homotopy equivalences of of degree 1. We prove that there exists an important map of to the set of homotopy classes . We relate with the set of smooth structures on by applying the surgery theory.
J. Math. Soc. Japan, Volume 53, Number 2 (2001), 357-382.
First available in Project Euclid: 9 June 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 58K15: Topological properties of mappings
Secondary: 57R45: Singularities of differentiable mappings 57R67: Surgery obstructions, Wall groups [See also 19J25] 57R55: Differentiable structures 55Q10: Stable homotopy groups
ANDO, Yoshifumi. Folding maps and the surgery theory on manifolds. J. Math. Soc. Japan 53 (2001), no. 2, 357--382. doi:10.2969/jmsj/05320357. https://projecteuclid.org/euclid.jmsj/1213023462