TY - JOUR

T1 - Self-intersection class for singularities and its application to fold maps

AU - Ohmoto, Toru

AU - Saeki, Osamu

AU - Sakuma, Kazuhiro

PY - 2003/9

Y1 - 2003/9

N2 - Let f : M → 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)) ∈ H* (M; 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.

AB - Let f : M → 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)) ∈ H* (M; 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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U2 - 10.1090/S0002-9947-03-03345-2

DO - 10.1090/S0002-9947-03-03345-2

M3 - Article

AN - SCOPUS:0042363657

VL - 355

SP - 3825

EP - 3838

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 9

ER -