689 research outputs found
Burnside obstructions to the Montesinos-Nakanishi 3-move conjecture
Yasutaka Nakanishi asked in 1981 whether a 3-move is an unknotting operation.
In Kirby's problem list, this question is called `The Montesinos-Nakanishi
3-move conjecture'. We define the n-th Burnside group of a link and use the 3rd
Burnside group to answer Nakanishi's question; ie, we show that some links
cannot be reduced to trivial links by 3-moves.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol6/paper11.abs.htm
Deformation of string topology into homotopy skein modules
Relations between the string topology of Chas and Sullivan and the homotopy
skein modules of Hoste and Przytycki are studied. This provides new insight
into the structure of homotopy skein modules and their meaning in the framework
of quantum topology. Our results can be considered as weak extensions to all
orientable 3-manifolds of classical results by Turaev and Goldman concerning
intersection and skein theory on oriented surfaces.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-34.abs.htm
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