Stable maps between 4-manifolds and elimination of their singularities

Osamu Saeki, Kazuhiro Sakuma

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let f:M→N be a stable map between orientable 4-manifolds, where M is closed and N is stably parallelisable. It is shown that the signature of M vanishes if and only if there exists a stable map g:M→N homotopic to f which has only fold and cusp singularities. This together with results of Ando and Èliašberg shows that, in this situation, the Thom polynomials are the only obstructions to the elimination of the singularities except for the fold singularity. Also studied are some topological properties (including those of the discriminant set) of stable maps between 4-manifolds with only Ak-type singularities.

Original languageEnglish
Pages (from-to)1117-1133
Number of pages17
JournalJournal of the London Mathematical Society
Volume59
Issue number3
DOIs
Publication statusPublished - Jan 1 1999

Fingerprint

Stable Map
4-manifold
Elimination
Singularity
Fold
Cusp
Topological Properties
Obstruction
Discriminant
Vanish
Signature
If and only if
Closed
Polynomial

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Stable maps between 4-manifolds and elimination of their singularities. / Saeki, Osamu; Sakuma, Kazuhiro.

In: Journal of the London Mathematical Society, Vol. 59, No. 3, 01.01.1999, p. 1117-1133.

Research output: Contribution to journalArticle

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