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Kei, Burnside groups, Fox colorings and tangle moves
(Joint with Mietek K. Dabkowski and Makiko Ishiwata)

Jozef H. Przytycki (the George Washington University)

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We search for invariants of links which are preserved by tangle moves (e.g. n-moves, rational moves,...). We can test any link invariant for its behavior under a tangle move. For rational moves the Burnside groups of links are the most useful (they are nonabelian generalizations of Fox colorings). The more general objects to use are Kei, introduced by Takasaki in 1942, however the interesting Kei (we call them Burnside Kei) are not well understood yet and the best tool is via core Kei of Burnside group. In particular we introduce the family of Kei Q(m,n) and ask for which values of $m$ and $n$ these Kei are finite.


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e-mail: [email protected], [email protected]


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