Impacto
Downloads
Downloads per month over past year
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
![]() |
PDF
Restringido a Repository staff only 527kB |
Official URL: http://cms.math.ca/cjm/v28/cjm1976v28.0161-0167.pdf
Abstract
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].
Item Type: | Article |
---|---|
Uncontrolled Keywords: | Topology of general 3-manifolds |
Subjects: | Sciences > Mathematics > Differential geometry |
ID Code: | 17266 |
Deposited On: | 29 Nov 2012 09:54 |
Last Modified: | 12 Dec 2018 15:14 |
Origin of downloads
Repository Staff Only: item control page