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

^*この研究の対応する著者

研究成果: Article › 査読

10 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	3825-3838
ページ数	14
ジャーナル	Transactions of the American Mathematical Society
巻	355
号	9
DOI	https://doi.org/10.1090/S0002-9947-03-03345-2
出版ステータス	Published - 2003 9月
外部発表	はい

ASJC Scopus subject areas

数学 (全般)
応用数学

文献へのアクセス

10.1090/S0002-9947-03-03345-2

他のファイルとリンク

引用スタイル

@article{10079a4773cf45ecbf275124a9294f5c,

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.",

keywords = "Fold map, Incident class, Pontrjagin class, Self-intersection class, Thom polynomial, Twisted coefficient",

author = "Toru Ohmoto and Osamu Saeki and Kazuhiro Sakuma",

year = "2003",

month = sep,

doi = "10.1090/S0002-9947-03-03345-2",

language = "English",

volume = "355",

pages = "3825--3838",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "9",

}

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.

KW - Fold map

KW - Incident class

KW - Pontrjagin class

KW - Self-intersection class

KW - Thom polynomial

KW - Twisted coefficient

UR - http://www.scopus.com/inward/record.url?scp=0042363657&partnerID=8YFLogxK

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

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

抄録

ASJC Scopus subject areas

文献へのアクセス

他のファイルとリンク

フィンガープリント

引用スタイル