Related papers: Irreducible 3-manifolds that cannot be obtained by…

This paper gives a proof that the universal cover of a closed 3-manifold built from three $\pi_1$-injective handlebodies is homeomorphic to $\mathbb R^3$. This construction is an extension to handlebodies of the conditions for gluing of…

We consider surgery moves along (n+1)-component Brunnian links in compact connected oriented 3-manifolds, where the framing of the each component is 1/k for k in Z. We show that no finite type invariant of degree < 2n-2 can detect such a…

In this paper, we define a new algebro-geometric invariant of 3-manifolds resulting from the Dehn surgery along a hyperbolic knot complement in S^3. We establish a Casson type invariant for these 3-manifolds. In the last section, we…

We call a pair (K, m) of a knot K in the 3-sphere S^3 and an integer m a Seifert fibered surgery if m-surgery on K yields a Seifert fiber space. For most known Seifert fibered surgeries (K, m), K can be embedded in a genus 2 Heegaard…

Non-isotopic Heegaard splittings of non-minimal genus were known previously only for very special 3-manifolds. We show in this paper that they are in fact a wide spread phenomenon in 3-manifold theory: We exhibit a large class of knots and…

We prove that for any non-trivial knot K, infinitely many r-surgeries K(r) along K have a unique surgery description along a knot. Moreover, we show that for any hyperbolic L-space knot K and infinitely many integer slopes n, the manifold…

We study finite type invariants of nullhomologous knots in a closed 3-manifold $M$ defined in terms of certain descending filtration $\{\mathscr{K}_n(M)\}_{n\geq 0}$ of the vector space $\mathscr{K}(M)$ spanned by isotopy classes of…

Let $M_n$ be a homology 3-sphere obtained by $\frac1n$-Dehn surgery along a $(p,q)$-torus knot. We consider a polynomial $\sigma_{(p,q,n)}(t)$ whose zeros are the inverses of the Reideimeister torsion of $M_n$ for…

In [arXiv:1405.6274, Question 5.2 & Question 5.3] Aschenbrenner, Friedl and Wilton ask: (1) Is the equation problem solvable for the fundamental group of any $3$-manifold? and (2) Is the first-order theory of the fundamental group of any…

For each connected alternating tangle, we provide an infinite family of non-left-orderable L-spaces. This gives further support for Conjecture [3] of Boyer, Gordon, and Watson that is a rational homology 3-sphere is an L-space if and only…

We are interested in knowing what type of manifolds are obtained by doing Dehn surgery on closed pure 3-braids in the 3-sphere. In particular, we want to determine when we get the 3-sphere by surgery on such a link. We consider links which…

We classify $SU(2)$-cyclic and $SU(2)$-abelian 3-manifolds, for which every representation of the fundamental group into $SU(2)$ has cyclic or abelian image respectively, among geometric 3-manifolds which are not hyperbolic. As an…

This article presents the constructions of new infinite families of smooth 4-manifolds with the property that any two manifolds in the same family are homeomorphic and, from their construction, seem to be quite different, but cannot be…

For a compact connected manifold M of dimension n greater than 3 and with no metric of positive scalar curvature, we prove that the Yamabe invariant is unchanged under surgery on spheres of dimension different from 1, n-2 and n-1. We use…

We prove that there are exactly $6$ Nil Seifert fibred spaces which can be obtained by Dehn surgeries on non-trefoil knots in $S^3$, with $\{60, 144, 156, 288, 300\}$ as the exact set of all such surgery slopes up to taking the mirror…

On every compact, orientable, irreducible 3-manifold V which is toroidal or has torus boundary components we construct a contact 1-form whose Reeb vector field R does not have any contractible periodic orbits and is tangent to the boundary.…

We find an infinite family of Seifert fibered surgeries on strongly invertible knots which do not have primitive/Seifert positions. Each member of the family is obtained from a trefoil knot after alternate twists along a pair of seiferters…

Let $\mathcal{Z}$ be a spin $4$-manifold carrying a parallel spinor and $M\hookrightarrow \mathcal{Z}$ a hypersurface. The second fundamental form of the embedding induces a flat metric connection on $TM$. Such flat connections satisfy a…

We construct two infinite families of knots each of which admits a Seifert fibered surgery with none of these surgeries coming from Dean's primitive/Seifert-fibered construction. This disproves a conjecture that all Seifert fibered…

Let K be a (2p,q)-torus knot and M_n is a 3-manifold obtained by 1/n-Dehn surgery along K. We consider a polynomial whose zeros are the inverses of the Reideimeister torsion of M_n for SL(2;C)-irreducible representations. Johnson gave a…