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2001 On holomorphic maps with only fold singularities
Yoshifumi Ando
Nagoya Math. J. 164: 147-184 (2001).

Abstract

Let $f:N\to P$ 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 $J^2(n, n; \mathbf{C})$, let $\Omega^{10}$ denote the space consisting of all 2-jets of regular map germs and fold map germs. In this paper we prove that $\Omega^{10}$ 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 $TN\oplus\theta_N$ to $TP\oplus\theta_P$, where $\theta_N$ and $\theta_P$ are the trivial line bundles.

Citation

Download Citation

Yoshifumi Ando. "On holomorphic maps with only fold singularities." Nagoya Math. J. 164 147 - 184, 2001.

Information

Published: 2001
First available in Project Euclid: 27 April 2005

zbMATH: 1037.58028
MathSciNet: MR1869099

Subjects:
Primary: 58K15
Secondary: 32S70, 57R45

Rights: Copyright © 2001 Editorial Board, Nagoya Mathematical Journal

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Vol.164 • 2001
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