Regular homotopy classes of immersions of 3-manifolds into 5-space

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dc.creatorSaeki, Osamu
dc.creatorSzűcs, András
dc.creatorTakase, Masamichi
dc.date2001-05-10
dc.date.accessioned2026-07-07T08:05:58Z
dc.date.available2026-07-07T08:05:58Z
dc.descriptionWe give geometric formulae which enable us to detect (completely in some cases) the regular homotopy class of an immersion with trivial normal bundle of a closed oriented 3-manifold into 5-space. These are analogues of the geometric formulae for the Smale invariants due to Ekholm and the second author. As a corollary, we show that two embeddings into 5-space of a closed oriented 3-manifold with no 2-torsion in the second cohomology are regularly homotopic if and only if they have Seifert surfaces with the same signature. We also show that there exist two embeddings $F_0$ and $F_8 : T^3 \hookrightarrow {\bf R}^5$ of the 3-torus $T^3$ with the following properties: (1) $F_0 \sharp h$ is regularly homotopic to $F_8$ for some immersion $h : S^3 \looparrowright {\bf R}^5$, and (2) the immersion $h$ as above cannot be chosen from a regular homotopy class containing an embedding.
dc.description16 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0105077
dc.identifierhttp://arxiv.org/abs/math/0105077
dc.identifierManuscripta Mathematica 108 (2002) pp.13-32
dc.identifierdoi:10.1007/s002290200251
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130452
dc.subjectGeometric Topology
dc.subject57R42 (Primary) 57M50, 57R45 (Secondary)
dc.titleRegular homotopy classes of immersions of 3-manifolds into 5-space
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