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Journal articles on the topic 'Dehn surgery'

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Published: 4 June 2021
Last updated: 14 February 2022

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1

Qiu, Ruifeng, and Zhang Ying. "∂-reducible Dehn surgery and annular Dehn surgery." Topology and its Applications 92, no. 1 (March 1999): 79–84. http://dx.doi.org/10.1016/s0166-8641(97)00229-0.

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2

Qiu, Ruifeng. "Reducible Dehn surgery and annular Dehn surgery." Pacific Journal of Mathematics 192, no. 2 (February 1, 2000): 357–68. http://dx.doi.org/10.2140/pjm.2000.192.357.

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3

Culler, Marc, C. McA Gordon, J. Luecke, and Peter B. Shalen. "Dehn Surgery on Knots." Annals of Mathematics 125, no. 2 (March 1987): 237. http://dx.doi.org/10.2307/1971311.

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4

Boyer, Steven. "Dehn surgery on knots." Chaos, Solitons & Fractals 9, no. 4-5 (April 1998): 657–70. http://dx.doi.org/10.1016/s0960-0779(97)00098-2.

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5

Culler, Marc, C. McA Gordon, J. Luecke, and Peter B. Shalen. "Dehn surgery on knots." Bulletin of the American Mathematical Society 13, no. 1 (July 1, 1985): 43–46. http://dx.doi.org/10.1090/s0273-0979-1985-15357-1.

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6

Lackenby, Marc. "Word hyperbolic Dehn surgery." Inventiones Mathematicae 140, no. 2 (May 1, 2000): 243–82. http://dx.doi.org/10.1007/s002220000047.

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7

Kang, Sungmo. "Hyperbolic tunnel-number-one knots with Seifert-fibered Dehn surgeries." Journal of Knot Theory and Its Ramifications 29, no. 11 (October 2020): 2050075. http://dx.doi.org/10.1142/s0218216520500753.

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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.
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8

Hayashi, Chuichiro. "Dehn surgery and essential annuli." Mathematical Proceedings of the Cambridge Philosophical Society 120, no. 1 (July 1996): 127–46. http://dx.doi.org/10.1017/s0305004100074727.

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In this paper we consider Dehn surgery and essential annuli whose two boundary components are in distinct components of the boundary of a 3-manifold.Let Nl be an orientable 3-manifold with boundary, Kl a knot in Nl, and N2 the 3-manifold obtained by performing γ-Dehn surgery Kl. In detail, let Vl be a regular neighbourhood Kl, X = Nl − int Vl the exterior of Kl, T the toral component ∂Vl of ∂X, and γ a slope on T. Then we obtain the 3-manifold N2 by attaching a solid torus V2 to X so that γ bounds a disc in V2. Let K2 be the core of V2. Let π be the slope of a meridian loop of Kl, and Δ the distance between the slopes π and γ, i.e. the minimal number of intersection points of the two slopes on T. Suppose for i = 1 and 2 that Ni contains a proper annulus Ai such that the two components of ∂Ai are essential loops on distinct incompressible components of ∂Ni. Then note that Ai is essential, i.e. incompressible and ∂-incompressible in Ni.
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9

Boyer, S., and X. Zhang. "Finite Dehn surgery on knots." Journal of the American Mathematical Society 9, no. 4 (1996): 1005–50. http://dx.doi.org/10.1090/s0894-0347-96-00201-9.

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10

Saveliev, Nikolai. "Dehn surgery along torus knots." Topology and its Applications 83, no. 3 (March 1998): 193–202. http://dx.doi.org/10.1016/s0166-8641(97)00109-0.

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11

Arslan, Aykut. "Dehn surgery on ribbon knots." Journal of Knot Theory and Its Ramifications 26, no. 11 (October 2017): 1750067. http://dx.doi.org/10.1142/s0218216517500675.

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In this paper, we show that if 0-surgery along a ribbon knot [Formula: see text] and 0-surgery along another knot [Formula: see text] give diffeomorphic 3-manifolds then [Formula: see text] has to be a slice knot. Moreover, they have diffeomorphic slice disk exteriors [Formula: see text] for some ribbon disk [Formula: see text] and slice disk [Formula: see text], where [Formula: see text] and [Formula: see text] are tubular neighborhoods of [Formula: see text] and [Formula: see text], respectively.
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12

Wu, Ying-Qing. "Dehn surgery on arborescent knots." Journal of Differential Geometry 43, no. 1 (1996): 171–97. http://dx.doi.org/10.4310/jdg/1214457901.

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13

Wu, Ying-Qing. "Dehn surgery on arborescent links." Transactions of the American Mathematical Society 351, no. 6 (February 5, 1999): 2275–94. http://dx.doi.org/10.1090/s0002-9947-99-02131-5.

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14

GHUMAN, SIMRAT M., LARRY M. GRANDA, and CHICHEN M. TSAU. "DEHN SURGERY ON SINGULAR KNOTS." Journal of Knot Theory and Its Ramifications 18, no. 04 (April 2009): 547–60. http://dx.doi.org/10.1142/s0218216509007051.

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In this paper we extend the idea of Dehn surgery to a singular knot with one singularity, and give conditions under which the surgery manifold of an untangled singular knot is a Haken manifold containing an incompressible torus. We then show that untangled singular knots have Property P.
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15

KADOKAMI, TERUHISA, and MASAFUMI SHIMOZAWA. "DEHN SURGERY ALONG TORUS LINKS." Journal of Knot Theory and Its Ramifications 19, no. 04 (April 2010): 489–502. http://dx.doi.org/10.1142/s0218216510007930.

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16

Bleiler, Steven A., and Richard A. Litherland. "Lens spaces and Dehn surgery." Proceedings of the American Mathematical Society 107, no. 4 (April 1, 1989): 1127. http://dx.doi.org/10.1090/s0002-9939-1989-0984783-3.

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17

Gordon, C. McA, and J. Luecke. "Reducible manifolds and Dehn surgery." Topology 35, no. 2 (April 1996): 385–409. http://dx.doi.org/10.1016/0040-9383(95)00016-x.

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18

Teragaito, Masakazu. "Dehn surgery on crosscap number two knots and projective planes." Journal of Knot Theory and Its Ramifications 11, no. 06 (September 2002): 869–86. http://dx.doi.org/10.1142/s0218216502002013.

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In the present paper, we will study the creation of projective planes by Dehn surgery on knots in the 3-sphere. It is shown that a projective plane cannot be created by Dehn surgery on a crosscap number two knot. As a corollary, we will prove that crosscap number two knots satisfy the projective space conjecture, which asserts that the projective 3-space cannot be obtained by Dehn surgery on a non-trivial knot in the 3-sphere.
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19

Culler, M., C. McA Gordon, J. Luecke, and P. B. Shalen. "Correction to: "Dehn Surgery on Knots"." Annals of Mathematics 127, no. 3 (May 1988): 663. http://dx.doi.org/10.2307/2007009.

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20

Agol, Ian, Marc Culler, and Peter B. Shalen. "Dehn surgery, homology and hyperbolic volume." Algebraic & Geometric Topology 6, no. 5 (December 8, 2006): 2297–312. http://dx.doi.org/10.2140/agt.2006.6.2297.

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21

Hodgson, Craig, and Steven Kerckhoff. "Universal bounds for hyperbolic Dehn surgery." Annals of Mathematics 162, no. 1 (July 1, 2005): 367–421. http://dx.doi.org/10.4007/annals.2005.162.367.

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22

Iwase, Zyun’iti. "Dehn-surgery along a torusT2-knot." Pacific Journal of Mathematics 133, no. 2 (June 1, 1988): 289–99. http://dx.doi.org/10.2140/pjm.1988.133.289.

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23

Wu, Ying-Qing. "Immersed essential surfaces and Dehn surgery." Topology 43, no. 2 (March 2004): 319–42. http://dx.doi.org/10.1016/s0040-9383(03)00046-6.

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24

Baker, Kenneth L., Cameron Gordon, and John Luecke. "Bridge number and integral Dehn surgery." Algebraic & Geometric Topology 16, no. 1 (February 23, 2016): 1–40. http://dx.doi.org/10.2140/agt.2016.16.1.

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25

Miyazak, Katura, and Kimihiko Motegixf. "Seifert fibred manifolds and Dehn surgery." Topology 36, no. 2 (March 1997): 579–603. http://dx.doi.org/10.1016/0040-9383(96)00009-2.

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26

TANGE, MOTOO. "Ozsváth Szabó's correction term and lens surgery." Mathematical Proceedings of the Cambridge Philosophical Society 146, no. 1 (January 2009): 119–34. http://dx.doi.org/10.1017/s0305004108001679.

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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.
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27

TERAGAITO, MASAKAZU. "CREATING KLEIN BOTTLES BY SURGERY ON KNOTS." Journal of Knot Theory and Its Ramifications 10, no. 05 (August 2001): 781–94. http://dx.doi.org/10.1142/s0218216501001153.

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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.
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28

Kim, Jin-Hong. "DEHN SURGERY AND A-POLYNOMIAL FOR KNOTS." Bulletin of the Korean Mathematical Society 43, no. 3 (August 1, 2006): 519–29. http://dx.doi.org/10.4134/bkms.2006.43.3.519.

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29

Hodgson, Craig, and Steven Kerckhoff. "The shape of hyperbolic Dehn surgery space." Geometry & Topology 12, no. 2 (May 12, 2008): 1033–90. http://dx.doi.org/10.2140/gt.2008.12.1033.

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30

Lackenby, Marc. "Dehn surgery on knots in 3-manifolds." Journal of the American Mathematical Society 10, no. 4 (1997): 835–64. http://dx.doi.org/10.1090/s0894-0347-97-00241-5.

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31

Clay, Adam, and Liam Watson. "Left-Orderable Fundamental Groups and Dehn Surgery." International Mathematics Research Notices 2013, no. 12 (May 10, 2012): 2862–90. http://dx.doi.org/10.1093/imrn/rns129.

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32

Shanahan, Patrick D. "Cyclic Dehn surgery and the A-polynomial." Topology and its Applications 108, no. 1 (November 2000): 7–36. http://dx.doi.org/10.1016/s0166-8641(99)00117-0.

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33

MATHIEU, Yves. "CLOSED 3–MANIFOLDS UNCHANGED BY DEHN SURGERY." Journal of Knot Theory and Its Ramifications 01, no. 03 (September 1992): 279–96. http://dx.doi.org/10.1142/s0218216592000161.

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If X is the space of the trefoil knot, we can find, for every integer e, two slopes on ∂X, ρe, γe, such that the Dehn fillings X (ρe) and X (γe) are homeomorphic 3-manifolds. The cores of the surgeries are inequivalent knots with homeomorphic complements. Analogous results are available if X is the knotspace of a 2-bridge torus knot. In an atoroidal homology sphere knots are determined by their complement if and only if hyperbolic knots are.
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34

Cooper, Daryl, and Marc Lackenby. "Dehn surgery and negatively curved 3-manifolds." Journal of Differential Geometry 50, no. 3 (1998): 591–624. http://dx.doi.org/10.4310/jdg/1214424971.

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35

Miyazaki, Katura, and Kimihiko Motegi. "Seifert fibered manifolds and Dehn surgery, III." Communications in Analysis and Geometry 7, no. 3 (1999): 551–82. http://dx.doi.org/10.4310/cag.1999.v7.n3.a3.

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36

Miyazaki, Katura, and Kimihiko Motegi. "Seifert fibered manifolds and Dehn surgery II." Mathematische Annalen 311, no. 4 (August 1, 1998): 647–64. http://dx.doi.org/10.1007/s002080050204.

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37

Wu, Ying-Qing. "Exceptional Dehn surgery on large arborescent knots." Pacific Journal of Mathematics 252, no. 1 (October 8, 2011): 219–43. http://dx.doi.org/10.2140/pjm.2011.252.219.

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38

Kim, Soo Hwan, and Yangkok Kim. "On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on Links." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–8. http://dx.doi.org/10.1155/2010/573403.

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We study the algebraic and geometric structures for closed orientable -manifolds obtained by Dehn surgery along the family of hyperbolic links with certain surgery coefficients and moreover, the geometric presentations of the fundamental group of these manifolds. We prove that our surgery manifolds are -fold cyclic covering of -sphere branched over certain link by applying the Montesinos theorem in Montesinos-Amilibia (1975). In particular, our result includes the topological classification of the closed -manifolds obtained by Dehn surgery on the Whitehead link, according to Mednykh and Vesnin (1998), and the hyperbolic link of components in Cavicchioli and Paoluzzi (2000).
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39

Curtis, Cynthia L. "A Dehn surgery description of regular finite cyclic covering spaces of rational homology spheres." Journal of Knot Theory and Its Ramifications 10, no. 03 (May 2001): 397–413. http://dx.doi.org/10.1142/s0218216501000925.

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We provide related Dehn surgery descriptions for rational homology spheres and a class of their regular finite cyclic covering spaces. As an application, we use the surgery descriptions to relate the Casson invariants of the covering spaces to that of the base space. Finally, we show that this places restrictions on the number of finite and cyclic Dehn fillings of the knot complements in the covering spaces beyond those imposed by Culler-Gordon-Luecke-Shalen and Boyer-Zhang.
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40

LI, WEIPING, and QINGXUE WANG. "AN SL2(ℂ) ALGEBRO-GEOMETRIC INVARIANT OF KNOTS." International Journal of Mathematics 22, no. 09 (September 2011): 1209–30. http://dx.doi.org/10.1142/s0129167x11007240.

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In this paper, we define a new algebro-geometric invariant of three-manifolds resulting from Dehn surgery along a hyperbolic knot complement in S3. We establish a Casson-type invariant for these three-manifolds. In the last section, we explicitly calculate the character variety of the figure-eight knot and discuss some applications, as well as the computation of our new invariants for some three-manifolds resulting from Dehn surgery along the figure-eight knot.
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41

Matignon, D., and N. Sayari. "Non-Orientable Surfaces and Dehn Surgeries." Canadian Journal of Mathematics 56, no. 5 (October 1, 2004): 1022–33. http://dx.doi.org/10.4153/cjm-2004-046-9.

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AbstractLet K be a knot in S3. This paper is devoted to Dehn surgeries which create 3-manifolds containing a closed non-orientable surface . We look at the slope p/q of the surgery, the Euler characteristic χ() of the surface and the intersection number s between and the core of the Dehn surgery. We prove that if χ() ≥ 15 – 3q, then s = 1. Furthermore, if s = 1 then q ≤ 4 – 3χ() or K is cabled and q ≤ 8 – 5χ(). As consequence, if K is hyperbolic and χ() = –1, then q ≤ 7.
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42

TRAN, Anh T. "Reidemeister Torsion and Dehn Surgery on Twist Knots." Tokyo Journal of Mathematics 39, no. 2 (December 2016): 517–26. http://dx.doi.org/10.3836/tjm/1484903134.

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43

Dowty, James G. "A new invariant on hyperbolic Dehn surgery space." Algebraic & Geometric Topology 2, no. 1 (June 22, 2002): 465–97. http://dx.doi.org/10.2140/agt.2002.2.465.

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44

Dean, John C. "Small Seifert-fibered Dehn surgery on hyperbolic knots." Algebraic & Geometric Topology 3, no. 1 (May 22, 2003): 435–72. http://dx.doi.org/10.2140/agt.2003.3.435.

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45

Baker, Kenneth L., Cameron Gordon, and John Luecke. "Obtaining genus 2 Heegaard splittings from Dehn surgery." Algebraic & Geometric Topology 13, no. 5 (July 5, 2013): 2471–634. http://dx.doi.org/10.2140/agt.2013.13.2471.

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46

Wu, Ying-Qing. "Dehn surgery on knots of wrapping number 2." Algebraic & Geometric Topology 13, no. 1 (March 6, 2013): 479–503. http://dx.doi.org/10.2140/agt.2013.13.479.

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47

Lakeland, Grant S., and Christopher J. Leininger. "Systoles and Dehn surgery for hyperbolic 3–manifolds." Algebraic & Geometric Topology 14, no. 3 (April 7, 2014): 1441–60. http://dx.doi.org/10.2140/agt.2014.14.1441.

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48

Lekili, Y., and T. Perutz. "Fukaya categories of the torus and Dehn surgery." Proceedings of the National Academy of Sciences 108, no. 20 (May 10, 2011): 8106–13. http://dx.doi.org/10.1073/pnas.1018918108.

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49

Parker, John R. "Book Review: Spherical CR geometry and Dehn surgery." Bulletin of the American Mathematical Society 46, no. 2 (December 23, 2008): 369–76. http://dx.doi.org/10.1090/s0273-0979-08-01226-3.

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50

Saito, Toshio. "Dehn surgery and (1,1)-knots in lens spaces." Topology and its Applications 154, no. 7 (April 2007): 1502–15. http://dx.doi.org/10.1016/j.topol.2006.02.008.

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