Obstructions to the existence of fold maps

被引：8

作者：

Sadykov, Rustam ^{[1
]}

Saeki, Osamu ^{[2
]}

Sakuma, Kazuhiro ^{[3
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

[2] Kyushu Univ, Fac Math, Nishi Ku, Fukuoka 8190395, Japan

[3] Kinki Univ, Dept Math, Osaka 5778502, Japan

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2010年 / 81卷

基金：

日本学术振兴会;

关键词：

SPECIAL GENERIC MAPS; THOM POLYNOMIALS; SMOOTH MAPPINGS; CO-HOMOLOGY; SINGULARITIES; ELIMINATION; 4-MANIFOLDS;

D O I：

10.1112/jlms/jdp072

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in terms of characteristic classes, which arise as Postnikov invariants, and can be interpreted as primary and secondary obstructions to the elimination of certain singularities. We also discuss the relationship between the existence problem of fold maps and that of vector fields of stabilized tangent bundles.

引用

页码：338 / 354

页数：17

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