A finite type invariant of order at most 4 for genus 2 handlebody-knots is a constant map

Atsushi Ishii,Kengo Kishimoto

doi:10.1016/j.topol.2011.11.018

A finite type invariant of order at most 4 for genus 2 handlebody-knots is a constant map

Atsushi Ishii, Kengo Kishimoto

https://doi.org/10.1016/j.topol.2011.11.018

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Journal: Topology and its Applications	Publication Date: Nov 15, 2011
Citations: 2	License type: elsevier-specific: oa user license

Affiliation: Osaka Institute of Technology, University of Tsukuba

#Constant Map #Space Of Invariants + Show 8 more

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Abstract

We show that a finite type invariant of order at most 4 for genus 2 handlebody-knots is a constant map. For this purpose, we give a concrete basis for the vector space of all finite type invariants of order at most 4 for spatial theta-curves, which makes a correction to Koikeʼs result. Each invariant of the basis is derived from the HOMFLYPT polynomial of the associated 3-component link of a spatial theta-curve.

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