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April, 2007 The homotopy principle for maps with singularities of given $\mathscr{K}$-invariant class
Yoshifumi ANDO
J. Math. Soc. Japan 59(2): 557-582 (April, 2007). DOI: 10.2969/jmsj/05920557


Let N and P be smooth manifolds of dimensions n and p respectively such that n p 2 or n < p . Let O N P denote an open subspace of J N P which consists of all regular jets and singular jets of certain given K -invariant class (including fold jets if n p ). An O -regular map f : N P refers to a smooth map such that j f ( N ) O N P . We will prove that a continuous section s of O N P over N has an O N P -regular map f such that s and j f are homotopic as sections. As an application we will prove this homotopy principle for maps with K -simple singularities of given class.


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Yoshifumi ANDO. "The homotopy principle for maps with singularities of given $\mathscr{K}$-invariant class." J. Math. Soc. Japan 59 (2) 557 - 582, April, 2007.


Published: April, 2007
First available in Project Euclid: 1 October 2007

zbMATH: 1126.58023
MathSciNet: MR2326177
Digital Object Identifier: 10.2969/jmsj/05920557

Primary: 58K30
Secondary: 57R45 , 58A20

Keywords: homotopy principle , K-simple , singularity

Rights: Copyright © 2007 Mathematical Society of Japan


Vol.59 • No. 2 • April, 2007
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