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

Toru Ohmoto; Osamu Saeki; Kazuhiro Sakuma

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

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

Toru Ohmoto^*, Osamu Saeki, Kazuhiro Sakuma

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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	https://doi.org/10.1090/S0002-9947-03-03345-2
Publication status	Published - 2003 Sept
Externally published	Yes

Keywords

Fold map
Incident class
Pontrjagin class
Self-intersection class
Thom polynomial
Twisted coefficient

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-03-03345-2

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title = "Self-intersection class for singularities and its application to fold maps",

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 Rim{\'a}nyi 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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author = "Toru Ohmoto and Osamu Saeki and Kazuhiro Sakuma",

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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.

KW - Fold map

KW - Incident class

KW - Pontrjagin class

KW - Self-intersection class

KW - Thom polynomial

KW - Twisted coefficient

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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 -

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

Abstract

Keywords

ASJC Scopus subject areas

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