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

Ohmoto, Toru; Saeki, Osamu; Sakuma, Kazuhiro

doi:10.1090/S0002-9947-03-03345-2

Self-intersection class for singularities and its application to fold maps
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by Toru Ohmoto, Osamu Saeki and Kazuhiro Sakuma

Trans. Amer. Math. Soc. 355 (2003), 3825-3838

DOI: https://doi.org/10.1090/S0002-9947-03-03345-2

Published electronically: 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 $S(f)$ 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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