Quantum Topology

By Michael Polyak. 2009

152 citations recorded by the source corpus.

It is well known that any two diagrams representing the same oriented link are related by a finite sequence of Reidemeister moves O1, O2 and O3. Depending on orientations of fragments involved in the moves, one may distinguish 4 different versions of each of the O1 and O2 moves, and 8 versions of the O3 move. We introduce a minimal generating set of four oriented Reidemeister moves, which includes two O1 moves, one O2 move, and one O3 move. We then study which other sets of up to 5 oriented moves generate all moves, and show that only few of them do. Some commonly considered sets are shown not to be generating. An unexpected non-equivalence of different O3 moves is discussed.

View Paper: https://www.semanticscholar.org/paper/37cda97f54a61db00e23c05ed3e20ada69d5f3b5

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Citations in the corpus

• A polynomial invariant of virtual links (2013, background): “According to [23], the following Reidemeister moves { Ω 1 a , Ω 1 b , Ω 2 a , Ω 3 a } is a generating set of all oriented Reidemeister moves.”