Stable maps between 4-manifolds and elimination of their singularities

Osamu Saeki, Kazuhiro Sakuma

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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
Issue number3
Publication statusPublished - Jun 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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