Transactions of the American Mathematical Society

Author(s): Toru Ohmoto; Osamu Saeki; Kazuhiro Sakuma
Journal: Trans. Amer. Math. Soc. 355 (2003), 3825-3838.
MSC (2000): Primary 57R45; Secondary 57R42
Posted: May 29, 2003
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Abstract: Let $f :M \to N$ be a generic smooth map with corank one singularities between manifolds, and let

be the singular point set of

. We define the self-intersection class $I(S(f)) \in H^*(M; \mathbf{Z})$ of

using an incident class introduced by Rimányi but with twisted coefficients, and give a formula for

in terms of characteristic classes of the manifolds. We then apply the formula to the existence problem of fold maps.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57R45, 57R42

Toru Ohmoto
Affiliation: Department of Mathematics and Computer Science, Faculty of Science, Kagoshima University, Koorimoto, Kagoshima 890-0065, Japan
Email: ohmoto@sci.kagoshima-u.ac.jp

Osamu Saeki
Affiliation: Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan
Email: saeki@math.kyushu-u.ac.jp

Kazuhiro Sakuma
Affiliation: Department of Mathematics and Physics, Faculty of Science and Technology, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan
Email: sakuma@math.kindai.ac.jp

DOI: 10.1090/S0002-9947-03-03345-2
PII: S 0002-9947(03)03345-2
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
Posted: 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
Copyright of article: Copyright 2003, American Mathematical Society

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