Related papers: SU(2)-cyclic surgeries and the pillowcase

We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S^3 (for any representation)…

Algebraic knots are known to be iterated torus knots and to admit L-space surgeries. However, Hedden proved that there are iterated torus knots that admit L-space surgeries but are not algebraic. We present an infinite family of such…

A knot in $S^3$ is rationally slice if it bounds a disk in a rational homology ball. We give an infinite family of rationally slice knots that are linearly independent in the knot concordance group. In particular, our examples are all…

For a knot K in S^3 we construct according to Casson--or more precisely taking into account Lin and Heusener's further works--a volume form on the SU(2)-representation space of the group of K. We prove that this volume form is a topological…

We show that all exceptional surgeries on hyperbolic alternating knots in the 3-sphere are integral surgeries.

Suppose that a hyperbolic knot in $S^3$ admits a finite surgery, Boyer and Zhang proved that the surgery slope must be either integral or half-integral, and they conjectured that the latter case does not happen. Using the correction terms…

We show that two-bridge knots and alternating fibered knots admit no purely cosmetic surgeries, i.e., no pair of distinct Dehn surgeries on such a knot produce 3-manifolds that are homeomorphic as oriented manifolds. Our argument, based on…

Myers shows that every compact, connected, orientable $3$--manifold with no $2$--sphere boundary components contains a hyperbolic knot. We use work of Ikeda with an observation of Adams-Reid to show that every $3$--manifold subject to the…

We give a complete classification of exceptional surgeries on hyperbolic alternating knots in the 3-sphere. As an appendix, we also show that the Montesinos knots M (-1/2, 2/5, 1/(2q + 1)) with q at least 5 have no non-trivial exceptional…

This thesis is concerned with the question of when the double branched cover of an alternating knot can arise by Dehn surgery on a knot in $S^3$. We approach this problem using a surgery obstruction, first developed by Greene, which…

In this article, we defined a knotted subgroup of a Lie group and considered a geometric notion of equivalence among them. We characterized these knotted subgroups in terms of one-parameter subgroups and provided examples in the case of…

Given an abelian group $A$ and a Lie group $G$, we construct a bilinear pairing from $A\times\pi_1({\mathcal R})$ to $\pi_1(G)$, where $\mathcal R$ is a subvariety of the variety of representations $A\to G$. In the case where $A$ is the…

We prove that the unreduced singular instanton homology $I^\sharp(Y,K;\mathbb{Z})$ has $2$-torsion for any null-homologous fibered knot $K$ of genus $g>0$ in a closed $3$-manifold $Y$ except for $\#^{2g}S^1\times S^2$. The main technical…

We show some computations on representations of the fundamental group in SL(2;C) and Reidemeister torsion for a homology 3-sphere obtained by Dehn surgery along the figure-eight knot. This is the second version. We recorrected several…

We show that if a surgery on a knot in a product sutured manifold yields the same product sutured manifold, then this knot is a 0-- or 1--crossing knot. The proof uses techniques from sutured manifold theory.

We show that the knot group of any knot in any integer homology sphere admits a non-abelian representation into $SU(3)$ such that meridians are mapped to matrices whose eigenvalues are the three distinct third roots of unity. This answers…

We show that for any positive integer $h$, a knot surgered elliptic surface $E(n)_{T(2,2h+1)}$ for a $(2,2h+1)$-torus knot $T(2,2h+1)$ and the elliptic surface $E(1)_{2,2h+1}$ admit handle decompositions without 1- and 3-handles using the…

For any knot $K$ in $S^3$ and any positive rational $r$, we show that smooth $(-r)$-surgery on $K$ always admits a tight contact structure. More specifically, the tightness is detected by the non-vanishing Heegaard Floer contact invariant.

Let $M$ be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if $M$ is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a…

Beginning with a $3$-manifold $M$ having a single torus boundary component, there are several computational techniques in the literature that use a presentation of the fundamental group of $M$ to produce infinite families of Dehn fillings…