scholarly journals Cusp shape and tunnel number

2018 ◽  
Vol 147 (3) ◽  
pp. 1351-1366
Author(s):  
Vinh Dang ◽  
Jessica S. Purcell
Keyword(s):  
Tunnel Number ◽  
Cusp Shape

464. Silicosis Prevention at New York City'S Water Tunnel Number Three

1999 ◽  
Author(s):  
J. Cocalis
Keyword(s):  
New York ◽  
Water Tunnel ◽  
Tunnel Number

scholarly journals There are no unexpected tunnel number one knots of genus one

2003 ◽  
Vol 356 (4) ◽  
pp. 1385-1442 ◽  
Author(s):  
Martin Scharlemann
Keyword(s):  
Tunnel Number ◽  
Genus One ◽  
Tunnel Number One Knots

Cusp-shape studies withHe+ions at 1.41- and 2.41-a.u. impact velocities

1992 ◽  
Vol 45 (7) ◽  
pp. 4535-4541 ◽  
Author(s):  
L. Gulyás ◽  
L. Sarkadi ◽  
J. Pálinkás ◽  
Á. Kövér ◽  
T. Vajnai ◽  
...  
Keyword(s):  
Cusp Shape

scholarly journals Tunnel number of tangles and knots

2014 ◽  
Vol 66 (4) ◽  
pp. 1303-1313 ◽  
Author(s):  
Toshio SAITO
Keyword(s):  
Tunnel Number

scholarly journals On composite tunnel number one links

1994 ◽  
Vol 59 (1) ◽  
pp. 59-71 ◽  
Author(s):  
Kanji Morimoto
Keyword(s):  
Tunnel Number

On the cusp shape of hyperbolic knots

2016 ◽  
Vol 25 (05) ◽  
pp. 1650025
Author(s):  
Yoshiyuki Yokota
Keyword(s):  
Potential Functions ◽  
Volume Conjecture ◽  
Cusp Shape

In this paper, we give a formula of the cusp shape of hyperbolic knots by using potential functions which appears in the study of the volume conjecture.

scholarly journals CHARACTER VARIETIES OF ONCE-PUNCTURED TORUS BUNDLES WITH TUNNEL NUMBER ONE

2013 ◽  
Vol 24 (06) ◽  
pp. 1350048 ◽  
Author(s):  
KENNETH L. BAKER ◽  
KATHLEEN L. PETERSEN
Keyword(s):  
Boundary Component ◽  
Lens Space ◽  
Algebraic Sets ◽  
Character Varieties ◽  
Torus Bundles ◽  
Whitehead Link ◽  
Birational Equivalence ◽  
Punctured Torus ◽  
Tunnel Number ◽  
Trace Fields

We determine the PSL2(ℂ) and SL2(ℂ) character varieties of the once-punctured torus bundles with tunnel number one, i.e. the once-punctured torus bundles that arise from filling one boundary component of the Whitehead link exterior. In particular, we determine "natural" models for these algebraic sets, identify them up to birational equivalence with smooth models, and compute the genera of the canonical components. This enables us to compare dilatations of the monodromies of these bundles with these genera. We also determine the minimal polynomials for the trace fields of these manifolds. Additionally, we study the action of the symmetries of these manifolds upon their character varieties, identify the characters of their lens space fillings, and compute the twisted Alexander polynomials for their representations to SL2(ℂ).

scholarly journals Knots with propretyR+

1983 ◽  
Vol 6 (3) ◽  
pp. 511-519
Author(s):  
Bradd Evans Clark
Keyword(s):  
Upper Bound ◽  
Connected Sum ◽  
Torus Knots ◽  
Heegaard Genus ◽  
High Tunnel ◽  
Tunnel Number

If we consider the set of manifolds that can be obtained by surgery on a fixed knotK, then we have an associated set of numbers corresponding to the Heegaard genus of these manifolds. It is known that there is an upper bound to this set of numbers. A knotKis said to have PropertyR+if longitudinal surgery yields a manifold of highest possible Heegaard genus among those obtainable by surgery onK. In this paper we show that torus knots,2-bridge knots, and knots which are the connected sum of arbitrarily many(2,m)-torus knots have PropertyR+It is shown that ifKis constructed from the tangles(B1,t1),(B2,t2),…,(Bn,tn)thenT(K)≤1+∑i=1nT(Bi,ti)whereT(K)is the tunnel ofKandT(Bi,ti)is the tunnel number of the tangle(Bi,ti). We show that there exist prime knots of arbitrarily high tunnel number that have PropertyR+and that manifolds of arbitrarily high Heegaard genus can be obtained by surgery on prime knots.

scholarly journals On the tunnel number and the Morse–Novikov number of knots

2010 ◽  
Vol 10 (2) ◽  
pp. 627-635 ◽  
Author(s):  
Andrei Pajitnov
Keyword(s):  
Tunnel Number
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