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Minimal plat representations of prime knots and links are not unique


Montesinos Amilibia, José María (1976) Minimal plat representations of prime knots and links are not unique. Canadian Journal of Mathematics-Journal Canadien de Mathématiques, 28 (1). pp. 161-167. ISSN 0008-414X

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J. S. Birman [same J. 28 (1976), no. 2, 264–290] has shown that any two plat representations of a link in S3 are stably equivalent and that stabilization is a necessary feature of the equivalence for certain composite knots. She has asked whether all 2n-plat representations of a prime link are equivalent. The author provides a negative answer, by exhibiting an infinite collection of prime knots and links in S3 in which each element L has at least two minimal and inequivalent 6-plat representations. In addition, as an application of another result of Birman [Knots, groups and 3-manifolds (Papers dedicated to the memory of R. H. Fox), pp. 137–164, Ann. of Math. Studies, No. 84, Princeton Univ. Press, Princeton, N.J., 1975], the 2-fold cyclic covering spaces of S3 branched over such links L form further examples of closed, orientable, prime 3-manifolds having inequivalent minimal Heegaard splittings, which were first constructed by Birman, F. González-Acuña and the author [Michigan Math. J. 23 (1976), no. 2, 97–103].

Tipo de documento:Artículo
Palabras clave:Topology of general 3-manifolds
Materias:Ciencias > Matemáticas > Geometría diferencial
Código ID:17266

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Última Modificación:07 Feb 2014 09:44

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