Related papers: Genus two Smale-Williams solenoids in 3-manifolds
Wieler has shown that every irreducible Smale space with totally disconnected stable sets is a solenoid (i.e., obtained via a stationary inverse limit construction). Using her construction, we show that the associated stable C*-algebra is…
Let $M$ be a closed, orientable, and irreducible 3-manifold with Heegaard genus two. We prove that if the fundamental group of $M$ is left-orderable then $M$ admits a co-orientable taut foliation.
By extending a result of Kronheimer-Mrowka to the family setting, we prove a gluing formula for the family Seiberg-Witten invariant. This formula allows one to compute the invariant for a smooth family of 4-manifolds by cutting it open…
Let M_1 and M_2 be compact, orientable 3-manifolds with incompressible boundary, and M the manifold obtained by gluing with a homeomorphism $\phi:\bdy M_1 \to \bdy M_2$. We analyze the relationship between the sets of low genus Heegaard…
We prove that $n$-sphere $\mathbb{S}^n$, $n\geq 2$, admits structurally stable diffeomorphisms $\mathbb{S}^n\to\mathbb{S}^n$ with non-orientable expanding attractors of any topological dimension $d\in\{1,\ldots,[\frac{n}{2}]\}$ where $[x]$…
Lens spaces are the only 3-manifolds that admit gradient-like flows with four fixed points. This is an immediate corollary of Morse inequality and of the Morse function with four critical points existence. A similar question for…
We define a trisection of a closed, orientable three dimensional manifold into three handlebodies, and a notion of stabilization for these trisections. Several examples of trisections are described in detail. We define the trisection genus…
This elementary article introduces easy-to-manage invariants of genus one knots in homology 3-spheres. To prove their invariance, we investigate properties of an invariant of 3-dimensional genus two homology handlebodies called the…
Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…
A family of one-vertex triangulations of 3-manifolds, layered-triangulations, is defined. Layered-triangulations are first described for handlebodies and then extended to all 3-manifolds via Heegaard splittings. A complete and detailed…
In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of…
The Heegaard genus is a fundamental invariant of 3-manifolds. However, computing the Heegaard genus of a triangulated 3-manifold is NP-hard, and while algorithms exist, little work has been done in making such an algorithm efficient and…
Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…
Motivated by a result of L.P. Roberts on rational blow-downs in Heegaard-Floer homology, we study such operations along 3-manifolds that arise as branched double covers of $S^{3}$ along several non-alternating, slice knots.
We study irreducible Smale spaces with totally disconnected stable sets and their associated $K$-theoretic invariants. Such Smale spaces arise as Wieler solenoids, and we restrict to those arising from open surjections. The paper follows…
An affine manifold is a manifold with an affine structure, i.e. a torsion-free flat affine connection. We show that the universal cover of a closed affine 3-manifold $M$ with holonomy group of shrinkable dimension (or discompacit\'e in…
This paper shows that there are symplectic four-manifolds M with the following property: a single isotopy class of smooth embedded two-spheres in M contains infinitely many Lagrangian submanifolds, no two of which are isotopic as Lagrangian…
Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. We…
We construct Bott-type and equivariant Seiberg-Witten Floer homology and cohomology for 3-manifolds, in particular rational homology spheres, and prove their diffeomorphism invariance. This paper is a revised version of math.DG/9701010.…
A Heegaard diagram for a 3-manifold M is a closed, oriented surface S together with a pair (X, Y) of compact 1-manifolds in S whose components serve as attaching curves for the 2-handles of the two sides of a Heegaard splitting for M. The…