An explicit relation between knot groups in lens spaces and those in S3
2018 ◽
Vol 27
(08)
◽
pp. 1850045
Keyword(s):
For a cyclic covering map [Formula: see text] between two pairs of a 3-manifold and a knot each, we describe the fundamental group [Formula: see text] in terms of [Formula: see text]. As a consequence, we give an alternative proof for the fact that certain knots in [Formula: see text] cannot be represented as the preimage of any knot in a lens space, which is related to free periods of knots. In our proofs, the subgroup of a group [Formula: see text] generated by the commutators and the [Formula: see text]th power of each element of [Formula: see text] plays a key role.
2006 ◽
Vol 15
(09)
◽
pp. 1119-1129
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2021 ◽
Vol 29
(6)
◽
pp. 863-868
Keyword(s):
2007 ◽
Vol 142
(2)
◽
pp. 259-268
◽
2007 ◽
Vol 75
(1)
◽
pp. 75-89
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2019 ◽
Vol 28
(08)
◽
pp. 1950049
◽
2011 ◽
Vol 20
(04)
◽
pp. 617-624
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2003 ◽
Vol 05
(06)
◽
pp. 967-982
◽
Keyword(s):
2017 ◽
Vol 26
(11)
◽
pp. 1750069
Keyword(s):