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Stronglycyclic branched coverings of (1, 1)knots and cyclic presentation of groups
, 2003
"... We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1,1)knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the nfold stronglycyclic branched coverings o ..."
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Cited by 14 (10 self)
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We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1,1)knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the nfold stronglycyclic branched coverings of (1,1)knots, through the elements of the mapping class group. We prove that every nfold stronglycyclic branched covering of a (1,1)knot admits a cyclic presentation for the fundamental group, arising from a Heegaard splitting of genus n. Moreover, we give an algorithm to produce the cyclic presentation and illustrate it in the case of cyclic branched coverings of torus knots of type (k,hk ± 1).
Stronglycyclic branched coverings of (1,1)knots and cyclic presentations of groups
, 2008
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and cyclic presentations of groups
, 2001
"... We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1, 1)knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the nfold stronglycyclic branched coverings ..."
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We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1, 1)knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the nfold stronglycyclic branched coverings of (1, 1)knots, through the elements of the mapping class group. We prove that every nfold stronglycyclic branched covering of a (1, 1)knot admits a cyclic presentation for the fundamental group, arising from a Heegaard splitting of genus n. Moreover, we give an algorithm to produce the cyclic presentation and illustrate it in the case of cyclic branched coverings of torus knots of type (k, hk ± 1). 1. Introduction and