Wirtinger presentations for higher dimensional manifold knots obtained from diagrams (Q2717749)
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scientific article; zbMATH DE number 1605337
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Wirtinger presentations for higher dimensional manifold knots obtained from diagrams |
scientific article; zbMATH DE number 1605337 |
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Wirtinger presentations for higher dimensional manifold knots obtained from diagrams (English)
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17 June 2001
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Wirtinger presentation
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knot group
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higher dimensional knot
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knot diagram
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broken surface diagram
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0.9055875
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0.8794129
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0.8763939
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0.87553084
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0.8719826
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0.8694665
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0.8692388
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0.8651758
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Wirtinger presentations allow a method of describing the fundamental group of a classical knot in 3-space and are read off a knot diagram. For oriented surfaces in 4-space, J. S. Carter and M. Saito have developed an analogue method to read Wirtinger relators of the fundamental group of the complement off a diagram. By modifying this method, making it work for any closed smooth or PL submanifold of dimension \(n\) in Euclidean \((n+2)\)-space, \(n\geq 2\), the author finds a way to construct a Wirtinger presentation of the fundamental group of the complement of the submanifold from a regular projection diagram. Local flatness of the submanifold is not required. Moreover, any such group can be realized by the corresponding group of a suitable surface in 4-space.
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