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April 2022 Join theorem for real analytic singularities
Kazumasa Inaba
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Osaka J. Math. 59(2): 403-416 (April 2022).

Abstract

Let $f_{1} : (\Bbb{R}^{n}, \mathbf{0}_{n}) \rightarrow (\Bbb{R}^{p}, \mathbf{0}_{p})$ and $f_{2} : (\Bbb{R}^{m}, \mathbf{0}_{m}) \rightarrow (\Bbb{R}^{p}, \mathbf{0}_{p})$ be analytic germs of independent variables, where $n, m \geq p \geq 2$. In this paper, we assume that $f_{1}, f_{2}$ and $f = f_{1} + f_{2}$ satisfy $a_{f}$-condition. Then we show that the tubular Milnor fiber of $f$ is homotopy equivalent to the join of tubular Milnor fibers of $f_1$ and $f_2$. If $p = 2$, the monodromy of the tubular Milnor fibration of $f$ is equal to the join of the monodromies of the tubular Milnor fibrations of $f_1$ and $f_2$ up to homotopy.

Acknowledgments

The author would like to thank Masaharu Ishikawa, Mutsuo Oka and Mihai Tibăr for precious comments and fruitful suggestions. He also thanks to the referee for careful reading of the manuscript and several accurate comments.

Citation

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Kazumasa Inaba. "Join theorem for real analytic singularities." Osaka J. Math. 59 (2) 403 - 416, April 2022.

Information

Received: 6 November 2020; Revised: 9 February 2021; Published: April 2022
First available in Project Euclid: 7 April 2022

Subjects:
Primary: 32S55
Secondary: 32S40 , 57K45

Rights: Copyright © 2022 Osaka University and Osaka City University, Departments of Mathematics

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Vol.59 • No. 2 • April 2022
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