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.
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.
"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