A Fox–Milnor theorem for knots in a thickened surface
2019 ◽
Vol 28
(12)
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pp. 1950073
Keyword(s):
A knot in a thickened surface [Formula: see text] is a smooth embedding [Formula: see text], where [Formula: see text] is a closed, connected, orientable surface. There is a bijective correspondence between knots in [Formula: see text] and knots in [Formula: see text], so one can view the study of knots in thickened surfaces as an extension of classical knot theory. An immediate question is if other classical definitions, concepts, and results extend or generalize to the study of knots in a thickened surface. One such famous result is the Fox–Milnor Theorem, which relates the Alexander polynomials of concordant knots. We prove a Fox–Milnor Theorem for concordant knots in a thickened surface by using Milnor torsion.
2006 ◽
Vol 15
(08)
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pp. 1079-1094
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2017 ◽
Vol 26
(09)
◽
pp. 1743007
Keyword(s):
2019 ◽
Vol 28
(06)
◽
pp. 1950039
Keyword(s):
2018 ◽
Vol 27
(04)
◽
pp. 1850026
2018 ◽
Keyword(s):