定値折り目特異点の消去II (可微分写像の特異点論の局所的研究と大域的研究)

Abstract

In this article, we first give a new simple proof to the elimination theorem of definite fold by homotopy for generic smooth maps of manifolds of dimension > 2 into the 2-sphere. Our new proof has the advantage that it is constructive and is also algorithmic: the procedures enable us to construct various explicit examples. Furthermore, we prove the non-existence of singular Legendrian fibrations on 3-manifolds, answering negatively to a question posed by Goo Ishikawa.