Moves on special spines
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 15 (2012), pp. 129-133
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The main theorem of the theory
of special spines states that any two spines of the same
3-manifold can be related be a sequence of moves $T^{\pm 1}$,
where
$T$ is performed in a regular neighborhood of an edge of a
spine and increases the number of its true vertices by one.
However, even in simple cases the proof of the theorem is not very helpful for finding
explicit sequences of moves. We describe here a first nontrivial example of
such sequence. The sequence relates two special spines of the
3-sphere with four removed 3-balls. This result answers a
question of Scott Carter, who wanted to get such sequence.
Keywords:
3-manifold, special spine, $2\to 3$ moves.
@article{VCHGU_2012_15_a10,
author = {S. V. Matveev},
title = {Moves on special spines},
journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
pages = {129--133},
publisher = {mathdoc},
number = {15},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a10/}
}
S. V. Matveev. Moves on special spines. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 15 (2012), pp. 129-133. http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a10/