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

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

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.

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.

scholarly journals Dehn surgery and (1,1)-knots in lens spaces

2007 ◽  
Vol 154 (7) ◽  
pp. 1502-1515 ◽  
Author(s):  
Toshio Saito
Keyword(s):  
Lens Spaces ◽  
Dehn Surgery

scholarly journals FOUR-DIMENSIONAL MANIFOLDS CONSTRUCTED BY LENS SPACE SURGERIES ALONG TORUS KNOTS

2012 ◽  
Vol 21 (11) ◽  
pp. 1250111 ◽  
Author(s):  
MOTOO TANGE ◽  
YUICHI YAMADA
Keyword(s):  
Lens Space ◽  
Complete List ◽  
Lens Spaces ◽  
Dehn Surgery ◽  
Integral Coefficient ◽  
Torus Knots ◽  
Kirby Calculus ◽  
Simply Connected

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 determine the complete list (set) of pairs of integral surgeries along distinct torus knots whose resulting manifolds are orientation preserving/reversing homeomorphic lens spaces, and study the closed 4-manifolds constructed as above. The list consists of five sequences. All framed links and Kirby calculus are indexed by integers. As a bi-product, some sequences of embeddings of lens spaces into the standard 4-manifolds are constructed.

REDUCIBLE DEHN SURGERY AND THE BRIDGE NUMBER OF A KNOT

2009 ◽  
Vol 18 (04) ◽  
pp. 493-504
Author(s):  
NABIL SAYARI
Keyword(s):  
Lens Spaces ◽  
Homology Sphere ◽  
Dehn Surgery ◽  
Connected Sum ◽  
Bridge Number

Let K be a knot in S3 and suppose that K(r) is a reducible manifold. Howie has proved that the number of connected summands is at most 3 [10, Corollary 5.3]. Furthermore, he showed that if K(r) is the connected sum of exactly three irreducible 3-manifolds, then K(r) = L(p1, q1)♯L(p2, q2)♯M, where L(p1, q1) and L(p2, q2) are a lens spaces and M is a ℤ-homology sphere. In this paper we study this specific case and we show that |r| ≤ (b-2)(b-1), for any knot with bridge number b.

scholarly journals Computations of Turaev-Viro-Ocneanu Invariants of 3-Manifolds from Subfactors

2003 ◽  
Vol 12 (04) ◽  
pp. 543-574 ◽  
Author(s):  
Nobuya Sato ◽  
Michihisa Wakui
Keyword(s):  
Lens Spaces ◽  
Dehn Surgery ◽  
Canonical Isomorphism ◽  
Linear Isomorphism ◽  
Surgery Formula ◽  
Sector Theory

In this paper, we establish a rigorous correspondence between the two tube algebras, that one comes from the Turaev-Viro-Ocneanu TQFT introduced by Ocneanu and another comes from the sector theory introduced by Izumi, and construct a canonical isomorphism between the centers of the two tube algebras, which is a conjugate linear isomorphism preserving the products of the two algebras and commuting with the actions of SL(2, Z). Via this correspondence and the Dehn surgery formula, we compute Turaev-Viro-Ocneanu invariants from several subfactors for basic 3-manifolds including lens spaces and Brieskorn 3-manifolds by using Izumi's data written in terms of sectors.

SPINAL KNOTS IN LENS SPACES

2006 ◽  
Vol 15 (10) ◽  
pp. 1371-1389
Author(s):  
ARNAUD DERUELLE ◽  
DANIEL MATIGNON
Keyword(s):  
Main Part ◽  
Lens Space ◽  
Lens Spaces ◽  
Dehn Surgery ◽  
Intersection Graphs ◽  
Möbius Band

A knot in a lens is said to be spinal if it can be isotoped on a standard spine (e.g. in ℝP3, spinal knots bound a Möbius band). We prove that a Dehn surgery on a non-spinal knot in a lens space cannot produce 𝕊3. With a view to study the Dehn surgeries that produce lens spaces, the main part is devoted to finding an obstruction for a standard spine to be minimal. We consider the intersection graphs coming from a standard spine and an arbitrary surface. This obstruction is given by the existence of a generalized Scharlemann cycle.

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