scholarly journals Ozsváth Szabó's correction term and lens surgery

2009 ◽  
Vol 146 (1) ◽  
pp. 119-134 ◽  
Author(s):  
MOTOO TANGE
Keyword(s):  
Explicit Formula ◽  
Correction Term ◽  
Lens Spaces ◽  
Dehn Surgery ◽  
Lens Surgery ◽  
Correction Terms

AbstractWe will give an explicit formula of Ozsváth–Szabó's correction terms of lens spaces. Applying the formula to a restriction studied by P. Ozsváth and Z. Szabó in [12] and [13], we obtain several constraints of lens spaces which are constructed by a positive Dehn surgery in 3-sphere. Some of the constraints are results which are analogous to results which were known in [6] and [20] before. The constraints completely determine knots yielding L(p, 1) by positive Dehn surgery.

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.

scholarly journals Lens spaces and Dehn surgery

1989 ◽  
Vol 107 (4) ◽  
pp. 1127-1127 ◽  
Author(s):  
Steven A. Bleiler ◽  
Richard A. Litherland
Keyword(s):  
Lens Spaces ◽  
Dehn Surgery

scholarly journals ON THE SPIN-REFINED RESHETIKHIN–TURAEV SU(2) INVARIANTS OF LENS SPACES

2012 ◽  
Vol 21 (10) ◽  
pp. 1250096
Author(s):  
KENTA OKAZAKI
Keyword(s):  
Explicit Formula ◽  
Lens Spaces

We give the explicit formula of the spin-refined Reshetikhin–Turaev SU(2) invariants of lens spaces. Using this result, we also give the formula of the spin-refined Turaev–Viro SU(2) invariants of lens spaces.

Four-dimensional manifolds constructed by lens space surgeries of distinct types

2017 ◽  
Vol 26 (11) ◽  
pp. 1750069
Author(s):  
Motoo Tange ◽  
Yuichi Yamada
Keyword(s):  
Fiber Surface ◽  
Lens Space ◽  
The Other ◽  
Lens Spaces ◽  
Dehn Surgery ◽  
Integral Coefficient ◽  
Torus Knots ◽  
Torus Knot ◽  
Simply Connected ◽  
Genus One

A framed knot with an integral coefficient determines a simply-connected 4-manifold by 2-handle attachment. Its boundary is a 3-manifold obtained by Dehn surgery along the framed knot. For a pair of such Dehn surgeries along distinct knots whose results are homeomorphic, it is a natural problem: Determine the closed 4-manifold obtained by pasting the 4-manifolds along their boundaries. We study pairs of lens space surgeries along distinct knots whose lens spaces (i.e. the resulting lens spaces of the surgeries) are orientation-preservingly or -reversingly homeomorphic. In the authors’ previous work, we treated with the case both knots are torus knots. In this paper, we focus on the case where one is a torus knot and the other is a Berge’s knot Type VII or VIII, in a genus one fiber surface. We determine the complete list (set) of such pairs of lens space surgeries and study the closed 4-manifolds constructed as above. The list consists of six sequences. All framed links and handle calculus are indexed by integers.

scholarly journals Knots yielding homeomorphic lens spaces by Dehn surgery

2010 ◽  
Vol 244 (1) ◽  
pp. 169-192 ◽  
Author(s):  
Toshio Saito ◽  
Masakazu Teragaito
Keyword(s):  
Lens Spaces ◽  
Dehn Surgery

Linear Optimal Control of a Linear System With State and Control Dependent Noise

1972 ◽  
Vol 94 (1) ◽  
pp. 34-40 ◽  
Author(s):  
P. J. McLane
Keyword(s):  
Optimal Control ◽  
Correction Term ◽  
Linear Feedback ◽  
System State ◽  
State Variables ◽  
Linear Optimal Control ◽  
Quadratic Minimization ◽  
Terminal Time ◽  
And Control ◽  
Correction Terms

A quadratic minimization problem for a linear stochastic system is solved in this paper. Both the finite and infinite terminal time cases are considered. Also two precise representations of the controlled stochastic process are considered. In one representation we include the correction term [6] for the state and control-dependent noise and in the other we do not. For the case with no correction terms, the optimal control is shown to be a linear feedback of the system state variables. Uniqueness and stability conditions are presented for this problem. The case with correction term is much harder to solve and we only determine the linear optimal control. An example is included which illustrates many results of the paper.

Effect of Quantum Inhomogeneity Corrections in Semi-Statistical Thomas–Fermi Calculations for Atoms

1974 ◽  
Vol 52 (19) ◽  
pp. 1926-1932 ◽  
Author(s):  
J. A. Stauffer ◽  
J. W. Darewych
Keyword(s):  
Dirac Equation ◽  
Variational Method ◽  
Quantum Correction ◽  
Correction Term ◽  
Approximate Solutions ◽  
The Other ◽  
Gradient Term ◽  
Gradient Expansion ◽  
Thomas Fermi ◽  
Correction Terms

Approximate solutions to the Thomas–Fermi equation with so-called 'quantum correction terms' have been obtained by the use of a variational method. The results for krypton support the conclusions of Tomishima and Yonei that the coefficient of the gradient term should be 9/5 of the value derived by Kirzhnits. On the other hand, when the use of these equations is restricted to a region of the atom where the gradient expansion of Kirzhnits might be expected to be valid, the Kirzhnits value of the constant gives the better results, but the best results are obtained with no correction term at all (i.e. with the Thomas–Fermi–Dirac equation).

The Absolute Value of The Chern-Simons-Witten Invariants of Lens Spaces

1995 ◽  
Vol 04 (02) ◽  
pp. 319-327 ◽  
Author(s):  
SHUJI YAMADA
Keyword(s):  
Explicit Formula ◽  
Lens Spaces ◽  
Homotopy Equivalence ◽  
Absolute Value ◽  
The Absolute ◽  
Chern Simons

An explicit formula for the absolute value of the Witten invariants is derived. We discuss the relation between homotopy equivalence and the absolute value of Witten invariants for lens spaces. We also give examples of arbitrarily finitely many lens spaces which have the same Witten invariants for any level r.

Homology of manifolds obtained by Dehn surgery on knots in lens spaces

2000 ◽  
Vol 09 (04) ◽  
pp. 431-442
Author(s):  
Antje Christensen
Keyword(s):  
Homology Group ◽  
Necessary Conditions ◽  
Lens Space ◽  
Lens Spaces ◽  
Dehn Surgery ◽  
Torus Knots

The question whether or not a Dehn surgery on a knot in a lens space yields a lens space of the same order is investigated with homological techniques. Determining the first homology group of the lens space after surgery and of its covering yields some necessary conditions on the knot and the surgery curve. Application of these results along with a calculation of Seifert invariants answers the question completely for surgery on torus knots along nullhomological curves.

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