Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 3825-3838 |
| Number of pages | 14 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 355 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - Jan 1 2003 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
Cite this
Self-intersection class for singularities and its application to fold maps. / Ohmoto, Toru; Saeki, Osamu; Sakuma, Kazuhiro.
In: Transactions of the American Mathematical Society, Vol. 355, No. 9, 01.01.2003, p. 3825-3838.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Self-intersection class for singularities and its application to fold maps
AU - Ohmoto, Toru
AU - Saeki, Osamu
AU - Sakuma, Kazuhiro
PY - 2003/1/1
Y1 - 2003/1/1
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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UR - http://www.scopus.com/inward/citedby.url?scp=0042363657&partnerID=8YFLogxK
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 -