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April, 2001 Folding maps and the surgery theory on manifolds
Yoshifumi ANDO
J. Math. Soc. Japan 53(2): 357-382 (April, 2001). DOI: 10.2969/jmsj/05320357


Let f:NP be a smooth map between n-dimensional oriented manifolds which has only folding singularities. Such a map is called a folding map. We prove that a folding map f : NP canonically determines the homotopy class of a bundle map of TNθN to TPθP, where θN and θP are the trivial line bundles over N and P respectively. When P is a closed manifold in addition, we define the set Ωfold(P) of all cobordism classes of folding maps of closed manifolds into P of degree 1 under a certain cobordism equivalence. Let SG denote the space limkSGk, where SGk denotes the space of all homotopy equivalences of Sk-1 of degree 1. We prove that there exists an important map of Ωfold(P) to the set of homotopy classes [P,SG]. We relate Ωfold(P) with the set of smooth structures on P by applying the surgery theory.


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Yoshifumi ANDO. "Folding maps and the surgery theory on manifolds." J. Math. Soc. Japan 53 (2) 357 - 382, April, 2001.


Published: April, 2001
First available in Project Euclid: 9 June 2008

zbMATH: 0980.58026
MathSciNet: MR1815139
Digital Object Identifier: 10.2969/jmsj/05320357

Primary: 58K15
Secondary: 55Q10 , 57R45 , 57R55 , 57R67

Keywords: Folding singularity , homotopy class , jet space , Manifold , surgery theory

Rights: Copyright © 2001 Mathematical Society of Japan


Vol.53 • No. 2 • April, 2001
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