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October 2021 On self-intersection of singularity sets of fold maps
Tatsuro SHIMIZU
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Hokkaido Math. J. 50(3): 297-308 (October 2021). DOI: 10.14492/hokmj/2018-935

Abstract

In this article, we give equations involving homology classes given by the self-intersection of singularity sets of fold maps. As an application, we give an obstruction to existence of fold maps up to cobordism.

Acknowledgment

The author expresses his appreciation to Professor Toru Ohomoto for his kind and helpful comments on Thom polynomials. The author would like to thank Professor Osamu Saeki and Professor Masamichi Takase for their helpful comments for singularity sets of smooth maps. The author also expresses his appreciation to Professor Kazuhiro Sakuma for his valuable comments and discussion about singularity sets and related topics. The author would also like to thank the referee for his/her valuable comments and suggestions. This work was supported by JSPS KAKENHI Grant Number JP18K13408.

Citation

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Tatsuro SHIMIZU. "On self-intersection of singularity sets of fold maps." Hokkaido Math. J. 50 (3) 297 - 308, October 2021. https://doi.org/10.14492/hokmj/2018-935

Information

Received: 26 November 2018; Revised: 21 April 2020; Published: October 2021
First available in Project Euclid: 17 December 2021

Digital Object Identifier: 10.14492/hokmj/2018-935

Subjects:
Primary: 57N80 , 57R25 , 57R45

Keywords: fold map , self intersection , singularity , Thom polynomial

Rights: Copyright c 2021 Hokkaido University, Department of Mathematics

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Vol.50 • No. 3 • October 2021
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