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 journalArticlepeer-review

9 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 languageEnglish
Pages (from-to)3825-3838
Number of pages14
JournalTransactions of the American Mathematical Society
Volume355
Issue number9
DOIs
Publication statusPublished - 2003 Sep
Externally publishedYes

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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