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Alexander invariants of periodic virtual knots
2018
Dissertationes Mathematicae
In this thesis, we show that every periodic virtual knot can be realized as the closure of a periodic virtual braid. If K is a q-periodic virtual knot with quotient K * , then the knot group G K * is a quotient of G K and we derive an explicit q-symmetric Wirtinger presentation for G K , whose quotient is a Wirtinger presentation for G K * . When K is an almost classical knot and q = p r , a prime power, we show that K * is also almost classical, and we establish a Murasugi-like congruence
doi:10.4064/dm785-3-2018
fatcat:rlfpfp4odrd3flw5vf2oacvbda