Virtual parity Alexander polynomial
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In this paper, we define the virtual Alexander polynomial following the works of Boden et al. (2016) [Alexander invariants for virtual knots, J. Knot Theory Ramications 24(3) (2015) 1550009] and Kaestner and Kauffman [Parity biquandles, in Knots in Poland. III. Part 1, Banach Center Publications, Vol. 100 (Polish Academy of Science Mathematical Institute, Warsaw, 2014), pp. 131–151]. The properties of this invariant are explored and some examples are computed. In particular, the invariant demonstrates that many virtual knots cannot be unknotted by crossing changes on only odd crossings.
2017 ◽
Vol 26
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pp. 1750007
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2016 ◽
Vol 25
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pp. 1650050
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2015 ◽
Vol 24
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pp. 1550009
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2012 ◽
Vol 21
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pp. 1250128
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2014 ◽
Vol 23
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pp. 1460011
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2013 ◽
Vol 22
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pp. 1341002
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2020 ◽
Vol 29
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pp. 2050088
2013 ◽
Vol 22
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pp. 1341003
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