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Minimal generating sets of Reidemeister moves
by
Piotr Suwara
University of Warsaw
Considering Reidemeister moves with orientation of strands, one obtains 16 different Reidemeister moves. It has been shown (Polyak 2010) that among these there is a set of 4 moves that generate all of them and the set is minimal.
One may consider the moves as directed - "forward" and "backward", obtaining 32 types of moves. For instance, "forward" Reidemeister moves of type I and II will be the ones that increase the number of crossings. The problem of finding a minimal generating set of these arises.
In the talk I will present the tools used to obtain Polyak's result and their application to the problem mentioned, how the new problem motivates the study of diagram invariants that are invariant under Reidemeister moves of type I and II, and some possible ways of constructing such diagram invariants.
Date received: December 2, 2014
Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-24.