TY - JOUR
T1 - Maps of manifolds into the plane which lift to standard embeddings in codimension two
AU - Carrara, V. L.
AU - Ruasc, M. A.S.
AU - Saeki, O.
N1 - Funding Information:
*Corresponding author. Partially supported by CNPq, FAPESP, and the Anglo-Japanese Scientific Programme, run by the Japan Society for the Promotion of Science and the Royal Society. E-mail addresses: vera@ime.usp.br (V.L. Carrara), maasruas@icmc.sc.usp.br (M.A.S. Ruas), saeki@math.sci.hiroshima-u.ac.jp (O. Saeki). 1Partially supported by CNPq and FAPESP.
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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.
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U2 - 10.1016/s0166-8641(99)00181-9
DO - 10.1016/s0166-8641(99)00181-9
M3 - Article
AN - SCOPUS:15944408469
SN - 0016-660X
VL - 110
SP - 265
EP - 287
JO - Topology and its Applications
JF - Topology and its Applications
IS - 3
ER -