On 1-handle surgery and finite type invariants of surface knots (Q1612205)
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scientific article; zbMATH DE number 1787525
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On 1-handle surgery and finite type invariants of surface knots |
scientific article; zbMATH DE number 1787525 |
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On 1-handle surgery and finite type invariants of surface knots (English)
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22 August 2002
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In this paper, a surface knot is a closed connected surface (possibly non-orientable) which is generically immersed in 4-space. The author defines a local operation called 1-handle surgery and he proves that this operation is an unknotting operation for generically immersed surfaces in 4-space. (In fact, the author proves here a non-orientable version of an unknotting theorem for oriented surfaces which he had proved in his paper [Osaka J. Math. 36, No. 1, 33-49 (1999; Zbl 0930.57029)].) The author uses then the operation of 1-handle surgery to investigate finite type invariants (in the form of Vassiliev modules) for generically immersed surfaces in 4-space.
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2-knot
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1-handle surgery
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unknotting operation
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Vassiliev invariant
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finite type invariant
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0.9230241
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0.90476155
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0.9040681
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0.90005136
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0.89795184
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0.8971662
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0.89176965
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