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
SN - 0002-9947
VL - 355
SP - 3825
EP - 3838
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 9
ER -