arXiv research

The geography problem is usually stated for simply connected symplectic 4-manifolds. When the first cohomology is nontrivial, however, one can restate the problem taking into account how close the symplectic manifold is to satisfying the conclusion of the Hard Lefschetz Theorem, which is measured by a nonnegative integ…

The geography of minimal symplectic 4-manifolds with arbitrary fundamental group and symplectic 6-manifolds with abelian fundamental group of small rank, and with arbitrary fundamental group are addressed.

In this note, the geography problem in dimension four is reviewed and then its extension to dimension six for the symplectic case is explained. Finally some examples in dimension six are provided.

In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds admitting several symplectic structures, inequivalent under deformation and sel…

The study creates symplectic Lefschetz fibrations and rational blowdowns for new 4-manifolds.

The geography and botany of smooth/symplectic nonspin 4-manifolds with abelian fundamental group are addressed.

Spin Lefschetz fibrations can represent any group and lattice point.

Constructs symplectic surface bundles with positive signatures.

In this paper, results of J. Park and of B.D Park and Szabo on simply connected symplectic 4-manifolds are re-proven and extended to non-simply connected manifolds using Luttinger surgeries.

Questions of geography of various classes of $4$-manifolds have been a central motivating question in $4$-manifold topology. Baykur and Korkmaz asked which small, simply connected, minimal $4$-manifolds admit a genus $2$ Lefschetz fibration. They were able to classify all the possible homeomorphism types and realize al…

In \cite{AP3, AHP}, the first author and his collaborators constructed the irreducible symplectic $4$-manifolds that are homeomorphic but not diffeomorphic to $(2n-1){\mathbb{CP}}^{2}\#(2n-1)\overline{\mathbb{CP}}^{2}$ for each integer $n \geq 25$, and the families of simply connected irreducible nonspin symplectic $4$…

The paper constructs exotic knotted surfaces and curves in 4-manifolds.

We prove that for any contact 3-manifold supported by a spinal open book decomposition with planar pages, there is a universal bound on the Euler characteristic and signature of its minimal symplectic fillings. The proof is an application of the spine removal surgery operation recently introduced in joint work of the a…

In this paper we construct a family of simply connected, spin, non-complex, symplectic 4-manifolds which cover all but finitely many allowed lattice points $(χ, c)$ lying in $0 \leq c \leq 8.76χ$. Furthermore, as a corollary, we prove that there exist infinitely many exotic smooth structures on $(2n+1)(S^2 \times S^2)$…

Study finds symplectic fillings' properties for specific contact covers.

Let X_1, X_2 be symplectic 4-manifolds containing symplectic surfaces F_1,F_2 of identical positive genus and opposite squares. Let Z denote the symplectic sum of X_1 and X_2 along the F_k. Using relative Gromov--Witten theory, we determine precisely when the symplectic 4-manifold Z is minimal (i.e., cannot be blown do…

We exhibit many examples of closed symplectic manifolds on which there is an autonomous Hamiltonian whose associated flow has no nonconstant periodic orbits (the only previous explicit example in the literature was the torus T^2n (n\geq 2) with an irrational symplectic structure). The underlying smooth manifolds of our…

Clarifies construction of K-contact non-Sasakian Smale-Barden manifolds.

New findings restrict Heegaard Floer homology for certain rational homology spheres.

We consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G_2 developed in math.DG/0012189. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors, the latter `matching' via a certain non-holomorphic map. Suitable examples of threefolds …

Geography problem for nonorientable surfaces bounded by knots.

Study on 4-manifolds with positive scalar curvature.

We investigate the tendency for financial instruments to form clusters when there are multiple factors influencing the correlation structure. Specifically, we consider a stock portfolio which contains companies from different industrial sectors, located in several different countries. Both sector membership and geograp…

New techniques create irreducible 4-manifolds with specific properties.

Delisle's projection explained by Euler in 18th century.

This work aims to study the Portuguese regional agglomeration process, using the linear form the New Economic Geography models that emphasize the importance of spatial factors (distance, costs of transport and communication) in explaining of the concentration of economic activity in certain locations. In a theoretical …

Khovanov homology invariant under Conway mutation.

Scoping review of EO-ML methods for causal inference in poverty geography.

Khovanov multicurves are restricted to linear components.

Lagrange's map construction ideas influenced later mathematicians.

Describes the Teichmüller stack and its variants, answering questions about orbifold points and local models.

The study explores relations between various knot invariants.

The paper characterizes Einstein 4-manifolds with semi-definite curvature and derives inequalities.

Geography effect is investigated for the Chinese stock market including the Shanghai and Shenzhen stock markets, based on the daily data of individual stocks. The Shanghai city and the Guangdong province can be identified in the stock geographical sector. By investigating a geographical correlation on a geographical pa…

We show that there exist non-formal compact oriented manifolds of dimension $n$ and with first Betti number $b_1=b\geq 0$ if and only if $n\geq 3$ and $b\geq 2$, or $n\geq (7-2b)$ and $0\leq b\leq 2$. Moreover, we present explicit examples for each one of these cases.

We prove that if a contact manifold $(M,ξ)$ is supported by a planar open book, then Euler characteristic and signature of any Stein filling of $(M,ξ)$ is bounded. We also prove a similar finiteness result for contact manifolds supported by spinal open books with planar pages. Moving beyond the geography of Stein filli…

The research community has increasing interest in autonomous driving research, despite the resource intensity of obtaining representative real world data. Existing self-driving datasets are limited in the scale and variation of the environments they capture, even though generalization within and between operating regio…

We investigate symmetry properties of peculiar modules, a Heegaard Floer invariant of 4-ended tangles which the author introduced in [arXiv:1712.05050]. In particular, we give an almost complete answer to the geography problem for components of peculiar modules of tangles. As a main application, we show that Conway mut…

Researchers propose a new approach to the Hopf problem for aspherical varieties.

Study shows non-trivial knot Floer homology for specific knots.

New method generates geolocated synthetic populations from real data.

New restrictions found on 4-manifolds with pinched curvature.

A compact oriented 4-manifold is defined to be of ``superconformal simple type'' if certain polynomials in the basic classes (constructed using the Seiberg-Witten invariants) vanish identically. We show that all known 4-manifolds of $b_2^+>1$ are of superconformal simple type, and that the numerical invariants of 4-man…

The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide nontrivial information about four-manifold topology. In particular, in the example …

This note shows every integer can be a signature of a hyperbolic 4-manifold.

With this work we try to analyse the agglomeration process in the Portuguese regions, using the New Economic Geography models. In these models the base idea is that where has increasing returns to scale in the manufactured industry and low transport costs, there is agglomeration. Of referring, as summary conclusion, th…

We give new obstructions to the module structures arising in Heegaard Floer homology. As a corollary, we characterize the possible modules arising as the Heegaard Floer homology of an integer homology sphere with one-dimensional reduced Floer homology. Up to absolute grading shifts, there are only two. We use this coro…

The aim of this paper is to analyze the relationship between inter-industry, intra-industry and inter-regional clustering and demand for labor by companies in Portugal. Is expected at the outset that there is more demand for work where the agglomeration is greater. It should be noted, as a summary conclusion, the resul…