Related papers: Splitting links by integer homology spheres
Let $n$, $q$ and $r$ be positive integers, and let $K_N^n$ be the $n$-skeleton of an $(N-1)$-simplex. We show that for $N$ sufficiently large every embedding of $K_N^n$ in $\mathbb{R}^{2n+1}$ contains a link $L_1\cup\cdots\cup L_r$…
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 construct an operator on sl(N) link homology with coefficients in a ring whose characteristic divides N. When P is prime, we use this operator to exhibit structural features of sl(P) link homology that are special to characteristic P…
We show that if a split link is obtained from a split link $L$ in $S^3$ by $1/n$-Dehn surgery along a trivial knot $C$, then the link $L\cup C$ is splittable. That is to say, it is impossible to obtain a split link from a split link via a…
The set of isotopy classes of ordered n-component links in the 3-sphere is acted on by the symmetric group via permutation of the components. The intrinsic symmetry group of the link, S(L), is defined to be the set of elements in the…
Conjecturally, a knot in the 3-sphere has only finitely many non-integer non-characterizing slopes. We verify this conjecture for all knots with knot Floer homology satisfying certain simplicity conditions. The class of knots satisfying our…
We show that the $\mathbb{Q}/\mathbb{Z}$-valued linking forms on rational homology spheres are (anti-) symmetric and we compute the linking form of a 3-dimensional rational homology sphere in terms of a Heegaard splitting. Both results have…
An immersed concordance between two links is a concordance with possible self-intersections. Given an immersed concordance we construct a smooth four-dimensional cobordism between surgeries on links. By applying $d$-invariant inequalities…
An invariant of orientable 3-manifolds is defined by taking the minimum $n$ such that a given 3-manifold embeds in the connected sum of $n$ copies of $S^2 \times S^2$, and we call this $n$ the embedding number of the 3-manifold. We give…
We construct an infinite family of knots in rational homology spheres with irreducible, non-fibered complements, for which every non-longitudinal filling is an L-space.
The theory of signature invariants of links in rational homology spheres is applied to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, an explicit formula is derived to compute…
Given a rational homology 3-sphere $M$, we introduce a triple linking form on $H_1(M; \mathbb{Z})$, defined when the classical torsion linking pairing of three homology classes vanishes pairwise. If $M$ is the boundary of a simply-connected…
The construction of knots via annular twisting has been used to create families of knots yielding the same manifold via Dehn surgery. Prior examples have all involved Dehn surgery where the surgery slope is an integral multiple of 2. In…
Let X be a 1-connected compact space such that the algebra H*(X;Z/2) is generated by one single element. We compute the cohomology of the free loop space H*(LX;Z/2) including the Steenrod algebra action. When X is a projective space CP^n,…
For a ring $R$, we denote by $R[\mathcal L]$ the free $R$-module spanned by the isotopy classes of singular links in $\mathbb S^3$. Given two invertible elements $x,t \in R$, the HOMFLY-PT skein module of singular links in $\mathbb S^3$…
We prove that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). For hyperbolic integer homology spheres this comes with the definition,…
We show that, for any integers, $g \geq 3$ and $n \geq 2$, there exists a link in $S^3$ such that its complement has a genus $g$ Heegaard splitting with distance $n$.
We derive an integral formula for the linking number of two submanifolds of the n-sphere S^n, of the product S^n x R^m, and of other manifolds which appear as "nice" hypersurfaces in Euclidean space. The formulas are geometrically…
This is the last of a series of papers which give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be homotopic in the link complement. The first paper of the series…
We first present three graphic surgery formulae for the degree $n$ part $Z_n$ of the Kontsevich-Kuperberg-Thurston universal finite type invariant of rational homology spheres. Each of these three formulae determines an alternate sum of the…