Regular homotopy classes of locally generic mappings

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• 作者：Juhá ; sz ; Andrá ; s
• 关键词：57R45 ; 58K30 ; 57R42 ; Immersion ; Locally generic mapping ; Regular homotopy ; Cross-cap singularity
• 刊名：Topology and its Applications
• 出版年：2004
• 出版时间：March 28, 2004
• 年：2004
• 卷：138
• 期：1-3
• 页码：45-59
• 全文大小：283 K

文摘

In this paper we generalize the notion of regular homotopy of immersions of a closed connected n-manifold into R²ⁿ⁻¹ to locally generic mappings. The main result is that if n=2 then two mappings with singularities are regularly homotopic if and only if they have the same number of cross-cap (or Whitney-umbrella) singularities. As an application, we get a description of the path-components of the space of those immersions of a surface into R⁴ whose projections into R³ are locally generic.