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2003 The universal order one invariant of framed knots in most $S^1$–bundles over orientable surfaces
Vladimir V Chernov
Algebr. Geom. Topol. 3(1): 89-101 (2003). DOI: 10.2140/agt.2003.3.89

Abstract

It is well-known that self-linking is the only –valued Vassiliev invariant of framed knots in S3. However for most 3–manifolds, in particular for the total spaces of S1–bundles over an orientable surface FS2, the space of –valued order one invariants is infinite dimensional. We give an explicit formula for the order one invariant I of framed knots in orientable total spaces of S1–bundles over an orientable not necessarily compact surface FS2. We show that if FS2,S1×S1, then I is the universal order one invariant, i.e. it distinguishes every two framed knots that can be distinguished by order one invariants with values in an Abelian group.

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Vladimir V Chernov. "The universal order one invariant of framed knots in most $S^1$–bundles over orientable surfaces." Algebr. Geom. Topol. 3 (1) 89 - 101, 2003. https://doi.org/10.2140/agt.2003.3.89

Information

Received: 3 December 2002; Accepted: 23 January 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1030.57019
MathSciNet: MR1997314
Digital Object Identifier: 10.2140/agt.2003.3.89

Subjects:
Primary: 57M27
Secondary: 53D99

Rights: Copyright © 2003 Mathematical Sciences Publishers

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