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We consider the question of extending a smooth homotopy coherent finite cyclic group action on the boundary of a smooth 4-manifold to its interior. As a result, we prove that Dehn twists along any Seifert homology sphere, except the…

Geometric Topology · Mathematics 2024-09-27 Sungkyung Kang , JungHwan Park , Masaki Taniguchi

We provide new examples of 3-manifolds with weight one fundamental group and the same integral homology as the lens space $L(2k,1)$ which are not surgery on any knot in the three-sphere. Our argument uses Furuta's 10/8-theorem, and is…

Geometric Topology · Mathematics 2024-05-28 Beibei Liu , Lisa Piccirillo

We consider the 3-manifold obtained by the 0-surgery along a double twist knot. We construct a candidate for a generalized torsion element in the fundamental group of the surged manifold, and see that there exists the cases where the…

Geometric Topology · Mathematics 2023-06-16 Nozomu Sekino

Let K be a non-trivial knot in the 3-sphere with a lens space surgery and L(p,q) a lens space obtained by a Dehn surgery on K. We study a relationship between the order of the fundamental group of L(p,q) and the Seifert genus of K.

Geometric Topology · Mathematics 2010-01-07 Toshio Saito

We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched covers of S^3 branched along links. The figure eight knot provides simple nontrivial examples. The groups arising in…

Geometric Topology · Mathematics 2016-09-07 Mieczyslaw K. Dabkowski , Jozef H. Przytycki , Amir A. Togha

We summarize and expand known connections between the study of Dehn surgery on links and the study of trisections of closed, smooth 4-manifolds. In addition, we describe how the potential counterexamples to the Generalized Property R…

Geometric Topology · Mathematics 2022-10-19 Jeffrey Meier , Alexander Zupan

We study Dehn twists in the outer automorphism group of a finitely generated non-abelian free group. Our main result states that, under certain compatibility conditions, sufficiently large powers of finitely many Dehn twists generate a…

Group Theory · Mathematics 2026-02-25 Donggyun Seo

We show that every irreducible toroidal integer homology sphere graph manifold has a left-orderable fundamental group. This is established by way of a specialization of a result due to Bludov and Glass for the almagamated products that…

Geometric Topology · Mathematics 2014-10-01 Adam Clay , Tye Lidman , Liam Watson

We give a complete classification of the Dehn surgeries on Montesinos knots which yield manifolds with cyclic or finite fundamental groups.

Geometric Topology · Mathematics 2014-10-01 Kazuhiro Ichihara , In Dae Jong

We prove that an HNN extension of a torsion-free nilpotent group is left-orderable. We also construct examples of non-left-orderable HNN extensions of left-orderable groups

Group Theory · Mathematics 2026-05-04 Azer Akhmedov , Cody Martin

Two Dehn surgeries on a knot are called {\it purely cosmetic}, if they yield manifolds that are homeomorphic as oriented manifolds. Suppose there exist purely cosmetic surgeries on a knot in $S^3$, we show that the two surgery slopes must…

Geometric Topology · Mathematics 2013-07-11 Yi Ni , Zhongtao Wu

For a 3-manifold with torus boundary admitting an appropriate involution, we show that Khovanov homology provides obstructions to certain exceptional Dehn fillings. For example, given a strongly invertible knot in S^3, we give obstructions…

Geometric Topology · Mathematics 2011-08-24 Liam Watson

Examples suggest that there is a correspondence between L-spaces and 3-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions for several large classes of such manifolds. In…

Geometric Topology · Mathematics 2011-07-26 Steven Boyer , Cameron McA. Gordon , Liam Watson

We determine the adjoint Reidemeister torsion of a $3$-manifold obtained by some Dehn surgery along $K$, where $K$ is either the figure-eight knot or the $5_2$-knot. As in a vanishing conjecture, we consider a similar conjecture and show…

Geometric Topology · Mathematics 2024-12-11 Naoko Wakijo

We classify Dehn surgeries on (p,q,r) pretzel knots that result in a manifold of finite fundamental group. The only hyperbolic pretzel knots that admit non-trivial finite surgeries are (-2,3,7) and (-2,3,9). Agol and Lackenby's 6-theorem…

Geometric Topology · Mathematics 2014-10-01 D. Futer , M. Ishikawa , Y. Kabaya , T. Mattman , K. Shimokawa

When can one 3-manifold be transformed to another by a finite sequence of Dehn surgeries which are restricted to preserve the first homology of the manifolds ? What is the resulting equivalence relation on 3-manifolds ? What if the surgery…

Geometric Topology · Mathematics 2010-04-06 Tim Cochran , Amir Gerges , Kent Orr

The main theorem of this paper is a generalisation of well known results about Dehn surgery to the case of attaching handlebodies to a simple 3-manifold. The existence of a finite set of `exceptional' curves on the boundary of the…

Geometric Topology · Mathematics 2014-11-11 Marc Lackenby

We give a Dehn surgery characterization of the trefoil and the figure eight knots. These results are gotten by combining surgery formulas in Heegaard Floer homology from an earlier paper with the characterization of these knots in terms of…

Geometric Topology · Mathematics 2007-05-23 Peter Ozsvath , Zoltan Szabo

We show that two Dehn surgeries on a knot $K$ never yield manifolds that are homeomorphic as oriented manifolds if $V_K''(1)\neq 0$ or $V_K'''(1)\neq 0$. As an application, we verify the cosmetic surgery conjecture for all knots with no…

Geometric Topology · Mathematics 2016-06-13 Kazuhiro Ichihara , Zhongtao Wu

We produce the first examples of closed, tight contact 3-manifolds which become overtwisted after performing admissible transverse surgeries. Along the way, we clarify the relationship between admissible transverse surgery and Legendrian…

Symplectic Geometry · Mathematics 2012-03-26 John A. Baldwin , John B. Etnyre