Related papers: Even and odd Kauffman bracket ideals for genus-1 t…

We use the Boothby-Wang fibration to construct certain simply connected K-contact manifolds and we give sufficient and necessary conditions on when such K-contact manifolds are homeomorphic to the odd dimensional spheres. If the symplectic…

Let S be a finite union of (pairwise disjoint but possibly knotted and linked) closed curves and tubes in the round sphere S^3 or in the flat torus T^3. In the case of the torus, S is further assumed to be contained in a contractible subset…

We study the standard family of supercurves of genus 1 with an underlying odd spin structures. We give a simple algebraic description of this family and of the compactified family of stable supercurves with one Neveu-Schwarz puncture. We…

It is shown that Legendrian (resp. transverse) cable links in the 3-sphere with its standard tight contact structure, i.e. links consisting of an unknot and a cable of that unknot, are classified by their oriented link type and the…

We introduce a new technique, based on Gaussian maps, to study the possibility, for a given surface, to lie on a threefold as a very ample divisor with given normal bundle. We give several applications, among which one to surfaces of…

We continue our study of ends non-compact manifolds. The over-arching aim is to provide an appropriate generalization of Siebenmann's famous collaring theorem that applies to manifolds having non-stable fundamental group systems at…

It is known that any tame hyperbolic 3-manifold with infinite volume and a single end is the geometric limit of a sequence of finite volume hyperbolic knot complements. Purcell and Souto showed that if the original manifold embeds in the…

We construct an infinite family of homology theories of framed links in thickened surfaces, as well as a homology theory whose graded Euler characteristic is exactly the Kauffman bracket of the link in the surface. Both theories are based…

This work considers the computation of controllable cut-and-paste groups $\mathrm{SKK}^{\xi}_n$ of manifolds with tangential structure $\xi:B_n\to BO_n$. To this end, we apply the work of Galatius-Madsen-Tillman-Weiss, Genauer and…

We formulate a relative analogue of the Clemens conjectures for 1/2-log Calabi-Yau threefold pairs (X,Y) (where K_X+2Y is isomorphic to O_X). This framework rests on the restoration of a perfect deformation/obstruction duality specific to…

It is known that any closed, exact Lagrangian in the cotangent bundle of a closed, smooth manifold is of the same homotopy type as the zero section. In this paper, we give a Fukaya-theoretic proof of this fact for the sphere and torus to…

We give a necessary and sufficient condition for the orientability of a locally standard 2-torus manifold with a fixed point which generalizes previous results of Nakayama-Nishimura in 2005 and Soprunova-Sottile in 2013. We construct…

For a compact, orientable, irreducible 3-manifold with toroidal boundary that is not the product of a torus and an interval or a cable space, each boundary torus has a finite set of slopes such that, if avoided, the Thurston norm of a Dehn…

Associated to an embedded surface in the $3$-sphere, we construct a diagram of fundamental groups, and prove that it is a complete invariant, wherefrom we deduce complete invariants of handlebody links, tunnels of handlebody links, and…

We study torus bundles with affine structure groups. First, we establish a rigidity result under constraints on the first Betti numbers: If $ \text{b}_{1}(M)-\text{b}_{1}(N)=\dim M-\dim N $ holds for a torus bundle $M$ with an affine…

We study some properties of decomposable exact Lagrangian cobordisms between Legendrian links in $\mathbb{R}^3$ with the standard contact structure. In particular, for any decomposable exact Lagrangian filling $L$ of a Legendrian link $K$,…

In this article, we completely classify torus bundles over the circle that bound 4-manifolds with the rational homology of the circle. Along the way, we classify certain integral surgeries along chain links that bound rational homology…

For each odd integer r greater than one and not divisible by three we give explicit examples of infinite families of simply and tangentially homotopy equivalent but pairwise non-homeomorphic closed homogeneous spaces with fundamental group…

It is known that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of "knot adjacency", studied in the paper…

The Kauffman bracket skein module $K(M)$ of a $3$-manifold $M$ is the quotient of the $\mathbb{Q}(A)$-vector space spanned by isotopy classes of links in $M$ by the Kauffman relations. A conjecture of Witten states that if $M$ is closed…