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On holomorphic maps with only fold singularities

Published online by Cambridge University Press:  22 January 2016

Yoshifumi Ando
Yoshifumi Ando*
Affiliation:
Department of Mathematics, Faculty of Science, Yamaguchi University, Yamaguchi, 753-8512, Japan, andoy@po.cc.yamaguchi-u.ac.jp
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Abstract

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Let f : N ≡ P be a holomorphic map between n-dimensional complex manifolds which has only fold singularities. Such a map is called a holomorphic fold map. In the complex 2-jet space J2(n,n;C), let Ω10 denote the space consisting of all 2-jets of regular map germs and fold map germs. In this paper we prove that Ω10 is homotopy equivalent to SU(n + 1). By using this result we prove that if the tangent bundles TN and TP are equipped with SU(n)-structures in addition, then a holomorphic fold map f canonically determines the homotopy class of an SU(n + 1)-bundle map of TN ⊕ θN to TP⊕ θP, where θN and θP are the trivial line bundles.

Keywords

58K1558A2058C10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 164 , December 2001 , pp. 147 - 184
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

References

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