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Differential 3-knots in 5-space with and without self-intersections
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
2001 (English)In: TOPOLOGY, ISSN 0040-9383, Vol. 40, no 1, 157-196 p.Article in journal (Refereed) Published
Abstract [en]

Regular homotopy classes of immersions $S^3 \to R^5$ constitute an infinite cyclic group. The classes containing embeddings form a subgroup of index 24. The obstruction for a generic immersion to be regularly homotopic to an embedding is described in terms of geometric invariants of its self-intersection. Geometric properties of self-intersections are used to construct two invariants J and St of generic immersions which are analogous to Arnold's invariants of plane curves [1]. We prove that J and St are independent first-order invariants and that any first-order invariant is a linear combination of these. As by-products, some invariants of immersions are obtained. Using them, we find restrictions on the topology of self-intersections

Place, publisher, year, edition, pages
2001. Vol. 40, no 1, 157-196 p.
Keyword [en]
immersion; self-intersection; finite type invariants; linking numbers; strangeness; IMMERSIONS
URN: urn:nbn:se:uu:diva-36582OAI: oai:DiVA.org:uu-36582DiVA: diva2:64481
Addresses: Ekholm T, Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden. Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden.Available from: 2008-06-11 Created: 2008-06-11 Last updated: 2011-01-13

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