Classification of knotted arcs in the thickenes punctured torus
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 15 (2012), pp. 112-118
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In the paper we classify knotted arcs in the thickened punctured torus $T_0\times I$. Arcs are constructed by a three-step process. First we enumerate graphs with 0, 1, 2 vertices of valence 4 and two vertices of valence 1, then for each graph we enumerate all corresponding knot projections, and after that we construct the corresponding minimal diagrams. For proving that all knotted arcs are different we use the generalized Kauffman polynomial.
Keywords:
knotted arc, thikened punctured torus.
@article{VCHGU_2012_15_a7,
author = {Ya. K. Ilyina},
title = {Classification of knotted arcs in the thickenes punctured torus},
journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
pages = {112--118},
publisher = {mathdoc},
number = {15},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a7/}
}
TY - JOUR AU - Ya. K. Ilyina TI - Classification of knotted arcs in the thickenes punctured torus JO - Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika PY - 2012 SP - 112 EP - 118 IS - 15 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a7/ LA - ru ID - VCHGU_2012_15_a7 ER -
%0 Journal Article %A Ya. K. Ilyina %T Classification of knotted arcs in the thickenes punctured torus %J Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika %D 2012 %P 112-118 %N 15 %I mathdoc %U http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a7/ %G ru %F VCHGU_2012_15_a7
Ya. K. Ilyina. Classification of knotted arcs in the thickenes punctured torus. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 15 (2012), pp. 112-118. http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a7/