Maps of manifolds into the plane which lift to standard embeddings in codimension two

V. L. Carrara, M. A.S. Ruasc, O. Saeki

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let f : M → ℝ2 be a smooth map of a closed n-dimensional manifold (n ≥ 2) into the plane and let π2n+2: ℝn+2 → ℝ2 be an orthogonal projection. We say that / has the standard lifting property, if every embedding f̃ : ℝn+2 with π2n+2 o f̃= f is standard in a certain sense. In this paper we give some sufficient conditions for a generic smooth map / to have the standard lifting property when M is a closed surface or an n-dimensional homotopy sphere.

Original languageEnglish
Pages (from-to)265-287
Number of pages23
JournalTopology and its Applications
Volume110
Issue number3
Publication statusPublished - Dec 1 2001
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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