Topology of ∑1, 1-singular maps

Abstract

0. IntroductionMorin [M] gave a local normal form for singular maps having almost maximal rank, where almost maximal means maximal minus 1. The aim of the present paper is to give a global version of his normal form. We concentrate here on the case of [sum ]1, 1, 0-singular maps. (For the definition see [Bo], [A–G–V], [G–G] and also here below.) The case of [sum ]1, 0 singular maps was considered by Haefliger in [Ha], see also [Sz1] and [Sz2]. For the motivation in finding such a global normal form see [Sz1], [Sz2], and the final remarks in this paper.