arXiv research

HabitatAgent offers a multi-agent system for transparent housing consultation.

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex sets. We propose a class of algorithms that perform both stochastic gradient desce…

CogMol designs novel drug-like molecules for SARS-CoV-2 targets.

SFAG generates realistic financial data that passes trading tests.

Study handles in 4-manifolds with cyclic fundamental group.

Elliptic surfaces without 1-handles proven for specific cases.

Study of 3-handle attachments in 4D manifolds using Kirby calculus.

The study shows conditions for elliptic surfaces without 1-handles.

Harer-Kas-Kirby conjectured that every handle decomposition of the elliptic surface E(1)_{2,3} requires both 1- and 3-handles. We prove that the elliptic surface E(n)_{p,q} has a handle decomposition without 1-handles for $n\geq 1$ and (p,q)=(2,3),(2,5),(3,4),(4,5).

We review Giroux's contact handles and contact handle attachments in dimension three and show that a bypass attachment consists of a pair of contact 1 and 2-handles. As an application we describe explicit contact handle decompositions of infinitely many pairwise non-isotopic overtwisted 3-spheres. We also give an alter…

D.Nash defined a family of homotopy 4-spheres in [11]. Proving that his manifolds ${\mathcal S}_{m,n,m',n'}$ are all real $S^4$, we find that they have handle decomposition with no 1-handles, two 2-handles and two 3-handles. The handle structures give new potential counterexamples of Property 2R conjecture.

New findings show infinitely many knots cannot be smoothly round handle slices.

A 2-dimensional braid over an oriented surface-knot $F$ is presented by a graph called a chart on a surface diagram of $F$. We consider 2-dimensional braids obtained by an addition of 1-handles equipped with chart loops. We introduce moves of 1-handles with chart loops, called 1-handle moves, and we investigate how muc…

Homology handles with trivial Alexander polynomial bound a 3D sphere.

The paper constructs contractible manifolds with knotted spheres.

Defines extended TQFTs using handle attachments.

Study handles in sutured manifolds and knots, finding varied handle numbers and unique surfaces.

The paper describes handle decompositions and Kirby diagrams for plane algebraic curves.

Handles decompositions reveal new open book structures.

Study shows knots surgered elliptic surfaces admit handle decompositions without 1- and 3-handles.

New $4$-manifolds without $1$- and $3$-handles are created from knots.

New 4-manifolds found without 1- and 3-handles.

We describe various handle moves in contact surgery diagrams, notably contact analogues of the Kirby moves. As an application of these handle moves, we discuss the respective classifications of long and loose Legendrian knots.

The study describes handle decompositions and Kirby diagrams for line arrangements.

J. Boyle classified 1-handles attached to surface-knots, that are closed and connected surfaces embedded in the Euclidean 4-space, in the case that the surfaces are oriented and 1-handles are orientable with respect to the orientations of the surfaces. In that case, the equivalence classes of 1-handles correspond to th…

A theorem on the existence of the unique minimal topologic handle decomposition of differentiable simply connected five-dimensional manifolds is proved. For a decomposition of this sort, the number of handles of each index is given.

We give an entirely geometric proof, without recourse to cellular homology, of the fact that $\partial^2=0$ in the chain complex defined by a handle decomposition of a given manifold. Topological invariance of the resulting `handle homology' is a consequence of Cerf theory.

New theorem connects handle-ribbon knots to slice derivatives.

Constructs exotic proper 2-knots from open 2-handles.

Study compact PL 4-manifolds with special handle decompositions.

The paper bounds the handle number of sutured manifolds using Morse-Novikov numbers and tunnel numbers.

The paper calculates a new invariant for 4-manifolds using handle decompositions and skein relations.

New insights into knot fusion numbers via cabling.

We determine the structure of the circular handle decompositions of the family of free genus one knots. Namely, if k is a free genus one knot, then the handle number h(k)= 0, 1 or 2, and, if k is not fibered (that is, if h(k)>0), then k is almost fibered. For this, we develop practical techniques to construct circular …

In this paper we construct Riemannian metrics and weight functions over Casson handles. We show that the corresponding Atiyah-Hitchin-Singer complexes are Fredholm for some class of Casson handles of bounded type. Using these, the Yang-Mills moduli spaces are constructed as finite dimensional smooth manifolds over Cass…

Proves complex homology three-spheres can be bounded by many handles.

Harer, Kas and Kirby have conjectured that every handle decomposition of the elliptic surface $E(1)_{2,3}$ requires both 1- and 3-handles. In this article, we construct a smooth 4-manifold which has the same Seiberg-Witten invariant as $E(1)_{2,3}$ and admits neither 1- nor 3-handles, by using rational blow-downs and K…

We present the Round Handle Problem, proposed by Freedman and Krushkal. It asks whether a collection of links, which contains the Generalised Borromean Rings, are slice in a 4-manifold R constructed from adding round handles to the four ball. A negative answer would contradict the union of the surgery conjecture and th…

Study maps 4-manifolds with 1-handles, revealing infinite rank centers.

Kirby color defined in Khovanov homology for 4D handlebodies.

Skein lasagna module calculates 4-manifold invariants using handle decompositions.

Given a rational homology sphere which bounds rational homology balls, we investigate the complexity of these balls as measured by the number of 1-handles in a handle decomposition. We use Casson-Gordon invariants to obtain lower bounds which also lead to lower bounds on the fusion number of ribbon knots. We use Levine…

We give new rational blowdown constructions of exotic CP^2#n(-CP^2) (5\leq n\leq 9) without using elliptic fibrations. We also show that our 4-manifolds admit handle decompositions without 1- and 3-handles, for 7\leq n\leq 9. A strategy for rational blowdown constructions of exotic CP^2#n(-CP^2) (1\leq n\leq 4) is also…

A standard convexity condition on the boundary of a symplectic manifold involves an induced positive contact form (and contact structure) on the boundary; the corresponding concavity condition involves an induced negative contact form. We present two methods of symplectically attaching 2-handles to convex boundaries of…

In this paper we give explicit, handle-by-handle constructions of concave symplectic fillings of all closed, oriented contact 3-manifolds. These constructions combine recent results of Giroux relating contact structures and open book decompositions of 3-manifolds, earlier results of the author on attaching 4-dimensiona…

GridPyM handles grid diagrams for knot theory.

Formulae for 1-3 handle attachments in 4-manifolds.

We prove that a positive definite smooth four-manifold with $b_2^+ \geq 2$ and having either no 1-handles or no 3-handles cannot admit a symplectic structure.