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Self-intersection class for singularities and its application to fold maps

Authors: Toru Ohmoto, Osamu Saeki and Kazuhiro Sakuma
Journal: Trans. Amer. Math. Soc. 355 (2003), 3825-3838
MSC (2000): Primary 57R45; Secondary 57R42
Published electronically: May 29, 2003
MathSciNet review: 1990176
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Abstract: Let $f :M \to N$ be a generic smooth map with corank one singularities between manifolds, and let $S(f)$ be the singular point set of $f$. We define the self-intersection class $I(S(f)) \in H^*(M; \mathbf{Z})$ of $S(f)$using an incident class introduced by Rimányi but with twisted coefficients, and give a formula for $I(S(f))$ in terms of characteristic classes of the manifolds. We then apply the formula to the existence problem of fold maps.

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Additional Information

Toru Ohmoto
Affiliation: Department of Mathematics and Computer Science, Faculty of Science, Kagoshima University, Koorimoto, Kagoshima 890-0065, Japan

Osamu Saeki
Affiliation: Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan

Kazuhiro Sakuma
Affiliation: Department of Mathematics and Physics, Faculty of Science and Technology, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan

Keywords: Self-intersection class, incident class, Thom polynomial, Pontrjagin class, twisted coefficient, fold map
Received by editor(s): September 12, 2002
Received by editor(s) in revised form: March 24, 2003
Published electronically: May 29, 2003
Additional Notes: The first author has been partially supported by Grant-in-Aid for Scientific Research (No. 12740046), the Ministry of Education, Science and Culture, Japan. The second and the third authors have been partially supported by Grant-in-Aid for Scientific Research (No. 13640076), the Ministry of Education, Science and Culture, Japan. The third author has also been partially supported by Grant for Encouragement of Young Researchers, Kinki Univ. (G008).
Dedicated: Dedicated to Professor Takuo Fukuda on the occasion of his 60th birthday
Article copyright: © Copyright 2003 American Mathematical Society

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