Topology of special generic maps of manifolds into Euclidean spaces

研究成果: ジャーナルへの寄稿学術誌査読

16 被引用数 (Scopus)

抄録

In this paper we study the global topology of special generic maps; i.e., smooth maps of closed n-manifolds into Rp (p<n) all of whose singularities are the definite fold points. Associated with a special generic map is the Stein factorization introduced in a paper of Burlet and de Rham, which is the space of the connected components of the fibers of the map. Our key idea is to reconstruct every special generic map from the Stein factorization, which enables us to obtain various topological restrictions imposed on the source manifolds and the singular sets. When p = 2, and when p = 3 and the source manifolds are 1-connected, we determine the diffeomorphism types of those manifolds which admit special generic maps into Rp, extending results of Burlet and de Rham and Porto and Furuya.

本文言語英語
ページ(範囲)265-293
ページ数29
ジャーナルTopology and its Applications
49
3
DOI
出版ステータス出版済み - 2月 26 1993
外部発表はい

!!!All Science Journal Classification (ASJC) codes

  • 幾何学とトポロジー

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