72 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
Homology operations on homology of quandles
We consider various homological operations on homology of quandles. We
introduce the notion of quandle partial derivatives, and extreme chains on
which appropriate partial derivatives vanish. Extreme chains yield homological
operations. We also consider the degree one homology operations created using
elements of the quandle satisfying the so-called -condition.Comment: 26 pages, 1 figur
A Generalization of the Gram determinant of type A
The Gram determinant of type was introduced by Lickorish in his work on
invariants of 3 - manifolds. We generalize the theory of the Gram determinant
of type by evaluating, in the annulus, a bilinear form of non-intersecting
connections in the disc. The main result provides a closed formula for this
Gram determinant. We conclude the paper by discussing Chen's conjecture about
the Gram determinant of type evaluated in the Klein bottle.Comment: 17 pages, 19 figure
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