1,721,132 research outputs found
Signature invariants of covering links
No full textWe apply the theory of signature invariants of links in rational homology spheres to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, we derive an explicit formula to compute signature invariants of their covering links. Using the formula, we produce fused boundary links that are positive mutants of ribbon links but are not concordant to boundary links. We also show that for any finite collection of patterns, there are homology boundary links that are not concordant to any homology boundary links admitting a pattern in the collection
Triple points of immersed surfaces in three dimensional manifolds
No full textThe number of triple points of a smoothly immersed surface in general position in a three dimensional manifold is congruent (mod 2) to the Euler characteristic of the surface plus the characteristic of the image of the surface. The Euler characteristic of the image is even if the immersed surface is null homologous with mod 2 coefficients. © 1989
THE FRAMED BRAID GROUP AND 3-MANIFOLDS
No full textThe framed braid group on n strands is defined to be a semidirect product of the braid group B(n) and Z(n) . Framed braids represent 3-manifolds in a manner analogous to the representation of links by braids. Consider two framed braids equivalent if they represent homeomorphic 3-manifolds. The main result of this paper is a Markov type theorem giving moves that generate this equivalence relation
Signatures of links in rational homology spheres
No full textA theory of signatures for odd-dimensional links in rational homology spheres is studied via their generalized Seifert surfaces. The jump functions of signatures are shown invariant under appropriately generalized concordance and a special care is given to accommodate one-dimensional links with mutual linking. Furthermore our concordance theory of links in rational homology spheres remains highly nontrivial after factoring out the contribution from links in integral homology spheres. (C) 2002 Elsevier Science Ltd. All rights reserved
Signature invariants of links from irregular covers and non-abelian covers
No full textSignature invariants of odd dimensional links from irregular covers and nonabelian covers of complements are obtained by using the technique of Casson and Gordon. We show that the invariants vanish fdr slice links and can be considered as invariants under F-m-link concordance. We illustrate examples of links that are not slice but behave as slice links for any invariants from abelian covers
On equivariant slice knots
No full textWe suggest a method to detect that two periodic knots are not equivariantly concordant, using surgery on factor links. We construct examples which satisfy all known necessary conditions for equivariant slice knots-Naik's and Choi-Ko-Song's improvements of classical results on Seifert forms and Casson-Gordon invariants of slice knots-but are not equivariantly slice
Genera of some closed 4-braids
No full textWe obtain the genera of knots or links that are the closures of certain types of 4-braids. These 4-braids are written as positive words in the band-generator presentation of the 4-braid group considered by E.S. Kang et al. in this volume, and their closures naturally bound surfaces that consist of four disks and half-twisted bands connecting any two disks. In fact we show that these spanning surfaces have the minimal genera. (C) 1997 Published by Elsevier Science B.V
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