Dehn surgery and Seifert surface systems

2017 ◽  
pp. 267-276
Author(s):  
Makoto Ozawa ◽  
Koya Shimokawa
Keyword(s):  
Dehn Surgery ◽  
Seifert Surface

Dehn surgeries on some classical links

2011 ◽  
Vol 54 (1) ◽  
pp. 33-45 ◽  
Author(s):  
Alberto Cavicchioli ◽  
Fulvia Spaggiari ◽  
Agnese Ilaria Telloni
Keyword(s):  
Dehn Surgery ◽  
Fundamental Groups ◽  
Branched Coverings ◽  
Borromean Rings

AbstractWe consider orientable closed connected 3-manifolds obtained by performing Dehn surgery on the components of some classical links such as Borromean rings and twisted Whitehead links. We find geometric presentations of their fundamental groups and describe many of them as 2-fold branched coverings of the 3-sphere. Finally, we obtain some topological applications on the manifolds given by exceptional surgeries on hyperbolic 2-bridge knots.

scholarly journals The shape of hyperbolic Dehn surgery space

2008 ◽  
Vol 12 (2) ◽  
pp. 1033-1090 ◽  
Author(s):  
Craig Hodgson ◽  
Steven Kerckhoff
Keyword(s):  
Dehn Surgery

CREATING KLEIN BOTTLES BY SURGERY ON KNOTS

2001 ◽  
Vol 10 (05) ◽  
pp. 781-794 ◽  
Author(s):  
MASAKAZU TERAGAITO
Keyword(s):  
Upper Bound ◽  
Klein Bottle ◽  
Dehn Surgery ◽  
The Creation ◽  
Genus One

In the present paper, we will study the creation of Klein bottles by Dehn surgery on knots in the 3-sphere, and we will give an upper bound for slopes creating Klein bottles for non-cabled knots by using the genera of knots. In particular, it is shown that if a Klein bottle is created by Dehn surgery on a genus one knot then the knot is a doubled knot. As a corollary, we obtain that genus one, cross-cap number two knots are doubled knot.

scholarly journals SEIFERT SURFACES, COMMUTATORS AND VASSILIEV INVARIANTS

2007 ◽  
Vol 16 (10) ◽  
pp. 1295-1329
Author(s):  
E. KALFAGIANNI ◽  
XIAO-SONG LIN
Keyword(s):  
Fundamental Group ◽  
Lower Central Series ◽  
Central Series ◽  
Seifert Surface ◽  
Vassiliev Invariants ◽  
Seifert Surfaces

We show that the Vassiliev invariants of a knot K, are obstructions to finding a regular Seifert surface, S, whose complement looks "simple" (e.g. like the complement of a disc) to the lower central series of its fundamental group. We also conjecture a characterization of knots whose invariants of all orders vanish in terms of their Seifert surfaces.

FORMULAS FOR THE CASSON INVARIANT OF CERTAIN INTEGRAL HOMOLOGY 3-SPHERES

2009 ◽  
Vol 18 (11) ◽  
pp. 1551-1576 ◽  
Author(s):  
SANG YOUL LEE ◽  
MYOUNGSOO SEO
Keyword(s):  
Explicit Formula ◽  
Dehn Surgery ◽  
Integral Homology ◽  
Integral Matrices ◽  
Knots And Links ◽  
Special Classes

In this paper, we introduce a representation of knots and links in S3 by integral matrices and then give an explicit formula for the Casson invariant for integral homology 3-spheres obtained from S3 by Dehn surgery along the knots and links represented by the integral matrices in which either all entries are even or the entries of each row are the same odd number. As applications, we study the preimage of the Casson invariant for a given integer and also give formulas for the Casson invariants of some special classes of integral homology 3-spheres.

4-Punctured Tori in the Exteriors of Knots

1997 ◽  
Vol 06 (05) ◽  
pp. 659-676 ◽  
Author(s):  
Mario Eudave-Muñoz
Keyword(s):  
Infinite Family ◽  
Solid Torus ◽  
Dehn Surgery ◽  
The Core

In this paper we construct an infinite family of hyperbolic knots, each having a Dehn surgery which produces a manifold containing an incompressible torus, which hits the core of the surgered solid torus in four points, but containing no incompressible torus hitting it in less than four points.

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