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.

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 Hyperbolic tunnel-number-one knots with Seifert-fibered Dehn surgeries

2020 ◽  
Vol 29 (11) ◽  
pp. 2050075
Author(s):  
Sungmo Kang
Keyword(s):  
Dehn Surgery ◽  
Surface Slope ◽  
Addition Formula ◽  
Closed Curves ◽  
Tunnel Number ◽  
Genus Two ◽  
Surgery Formula ◽  
Tunnel Number One Knots

Suppose [Formula: see text] and [Formula: see text] are disjoint simple closed curves in the boundary of a genus two handlebody [Formula: see text] such that [Formula: see text] (i.e. a 2-handle addition along [Formula: see text]) embeds in [Formula: see text] as the exterior of a hyperbolic knot [Formula: see text] (thus, [Formula: see text] is a tunnel-number-one knot), and [Formula: see text] is Seifert in [Formula: see text] (i.e. a 2-handle addition [Formula: see text] is a Seifert-fibered space) and not the meridian of [Formula: see text]. Then for a slope [Formula: see text] of [Formula: see text] represented by [Formula: see text], [Formula: see text]-Dehn surgery [Formula: see text] is a Seifert-fibered space. Such a construction of Seifert-fibered Dehn surgeries generalizes that of Seifert-fibered Dehn surgeries arising from primtive/Seifert positions of a knot, which was introduced in [J. Dean, Small Seifert-fibered Dehn surgery on hyperbolic knots, Algebr. Geom. Topol. 3 (2003) 435–472.]. In this paper, we show that there exists a meridional curve [Formula: see text] of [Formula: see text] (or [Formula: see text]) in [Formula: see text] such that [Formula: see text] intersects [Formula: see text] transversely in exactly one point. It follows that such a construction of a Seifert-fibered Dehn surgery [Formula: see text] can arise from a primitive/Seifert position of [Formula: see text] with [Formula: see text] its surface-slope. This result supports partially the two conjectures: (1) any Seifert-fibered surgery on a hyperbolic knot in [Formula: see text] is integral, and (2) any Seifert-fibered surgery on a hyperbolic tunnel-number-one knot arises from a primitive/Seifert position whose surface slope corresponds to the surgery slope.

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.

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