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Stable Maps between 4-Manifolds and Elimination of their Singularities
Authors:Saeki  Osamu; Sakuma  Kazuhiro
Institution:Department of Mathematics, Faculty of Science, Hiroshima University Higashi-Hiroshima 739-8526, Japan, saeki{at}math.sci.hiroshima-u.ac.jp
Department of General Education, Kochi National College of Technology Nankoku-City, Kochi 793-8502, Japan, sakuma{at}ge.kochi-ct.ac.jp
Abstract:Let f:M->N be a stable map between orientable 4-manifolds, whereM is closed and N is stably parallelisable. It is shown thatthe signature of M vanishes if and only if there exists a stablemap g:M->N homotopic to f which has only fold and cusp singularities.This together with results of Ando and Èliasberg showsthat, in this situation, the Thom polynomials are the only obstructionsto the elimination of the singularities except for the foldsingularity. Also studied are some topological properties (includingthose of the discriminant set) of stable maps between 4-manifoldswith only Ak-type singularities.
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