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STABLE MAPS BETWEEN 4-MANIFOLDS AND ELIMINATION OF THEIR SINGULARITIES

Published online by Cambridge University Press:  01 June 1999

OSAMU SAEKI  and
KAZUHIRO SAKUMA
OSAMU SAEKI
Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan, saeki@math.sci.hiroshima-u.ac.jp
KAZUHIRO SAKUMA
Affiliation:
Department of General Education, Kochi National College of Technology, Nankoku-City, Kochi 793-8502, Japan, sakuma@ge.kochi-ct.ac.jp Current address: Department of Mathematics and Physics, Faculty of Science and Engineering, Kinki University, Higashi-Osaka 577-8502, Japan, sakuma@math.kindai.ac.jp
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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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 1117 - 1133
Copyright
The London Mathematical Society 1999

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