arXiv research

Compact Kähler manifolds with positive curvature have contractible covers.

In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essential coverings by contractible metric balls, and provide a uniform bound on the numbers of contractible metric balls formi…

This paper gives a new proof of a result of Geoghegan and Mihalik which states that whenever a contractible open $n$-manifold $W$ which is not homeomorphic to $\mathbf{R}^n$ is a covering space of an $n$-manifold $M$ and either $n \geq 4$ or $n=3$ and $W$ is irreducible, then the group of covering translations injects …

This paper concerns the class of contractible open 3-manifolds which are ``locally finite strong end sums'' of eventually end-irreducible Whitehead manifolds. It is shown that whenever a 3-manifold in this class is a covering space of another 3-manifold the group of covering translations must be a free group. It follow…

This paper uses Brin and Thickstun's theory of end reductions of non-compact 3-manifolds to study groups of covering translations of irreducible contractible open 3-manifolds W which are not homeomorphic to R^3. We associate to W an object S(W) called the simplicial complex of minimal R^2-irreducible end reductions of …

In this paper we deduce a local deformation lemma for uniform embeddings in a metric covering space over a compact manifold from the deformation lemma for embeddings of a compact subspace in a manifold. This implies the local contractibility of the group of uniform homeomorphisms of such a metric covering space under t…

The article classifies cubiquitous sublattices and applies them to branched covers.

A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were studied intensively. Our main result is that intersection patterns of good covers are …

By a construction of Berstein and Edmonds every proper branched cover f between manifolds is a factor of a branched covering orbit map from a locally connected and locally compact Hausdorff space called the monodromy space of f to the target manifold. For proper branched covers between 2-manifolds the monodromy space i…

Given an irreducible contractible open 3-manifold W which is not homeomorphic to R^3, there is an associated simplicial complex S(W), the complex of end reductions of W. Whenever W covers a 3-manifold M one has that the fundamental group of M is isomorphic to a subgroup of the group Aut(S(W)) of simplicial automorphism…

This paper gives a description of the full space of Bridgeland stability conditions on the bounded derived category of a contraction algebra associated to a 3-fold flop. The main result is that the stability manifold is the universal cover of a naturally associated hyperplane arrangement, which is known to be simplicia…

Suppose $M$ is a closed, connected, orientable, \irr\ \3m\ such that $G=π_1(M)$ is infinite. One consequence of Thurston's geometrization conjecture is that the universal covering space $\widetilde{M}$ of $M$ must be \homeo\ to $\RRR$. This has been verified directly under several different additional assumptions on $G…

The paper analyzes game theory in convertible contracts during liquidity events.

In a previous paper, we showed nonvaninishing of the universal index elements in the K-theory of the maximal C*-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from the first relevant paper of Gromov and Lawson, involving contracting maps defined on …

Bayesian analysis shows unlabeled data improve graph-based semi-supervised learning.

Research shows RCD* spaces are semi-locally simply connected.

We depart from the usual methods for pricing contracts with the counterparty credit risk found in most of the existing literature. In effect, typically, these models do not account for either systemic effects or at-first-default contagion and postulate that the contract value at default equals either the risk-free valu…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively curved, locally symmetric manifold. Another application is the classification of a…

Bernard et al. (2015) study an optimal insurance design problem where an individual's preference is of the rank-dependent utility (RDU) type, and show that in general an optimal contract covers both large and small losses. However, their contracts suffer from a problem of moral hazard for paying more compensation for a…

We prove a "gluing" theorem for monotone homotopies; a monotone homotopy is a homotopy through simple contractible closed curves which themselves are pairwise disjoint. We show that two monotone homotopies which have appropriate overlap can be replaced by a single monotone homotopy. The ideas used to prove this theorem…

The aim of this paper is to introduce an insurance model allowing reinsurance and dividend payment. Our model deals with several homogeneous contracts and takes into account the legislation regarding the provisions to be justified by the insurance companies. This translates into some restriction on the (maximal) number…

The study provides a generalization bound for a family of implicit networks.

Let $G$ and $H$ be two groups acting on path connected topological spaces $X$ and $Y$ respectively. Assume that $H$ is finite of order $m$ and the quotient maps $p:X\to X/G$ and $q:Y\to Y/H$ are regular coverings. Then it is well-known that the wreath product $G\wr H$ naturally acts on $W = X^m\times Y$, so that the qu…

Proves properties of complex algebraic varieties and local systems.

New MKABSDEs help calculate initial margins in financial contracts.

The paper proves a conjecture about manifold limits and characterizes their structure.

This article announces joint work with Frank Connolly and Jim Davis. We generalize our classification of pseudo-free involutions on the n-torus, by studying the action of the associated infinite group with torsion in the universal cover. Included is a non-Riemannian example obtained from the restriction of the action o…

We use methods from network science to analyze corruption risk in a large administrative dataset of over 4 million public procurement contracts from European Union member states covering the years 2008-2016. By mapping procurement markets as bipartite networks of issuers and winners of contracts we can visualize and de…

We investigate the problem of pricing and hedging derivatives of Electricity Futures contract when the underlying asset is not available. We propose to use a cross hedging strategy based on the Futures contract covering the larger delivery period. A quick overview of market data shows a basis risk for this market incom…

Abstract framework for cross-currency interest rate contracts.

We study the curvature of metric spaces and branched covers of Riemannian manifolds, with applications in topology and algebraic geometry. Here curvature bounds are expressed in terms of the CAT(k) inequality. We prove a general CAT(k) extension theorem, giving sufficient conditions on and near the boundary of a locall…

Study on Ricci flows of awesome homogeneous spaces, proving finite extinction time.

About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature. These manifolds are thus elements of {\em hyperbolic geometry}, as natural as Euclid's regular polyhedra. For a closed manifold, Mostow rigidity assures that a hyperbolic structure is unique when it ex…

Majorizing measures control sequential complexities for online learning.

We consider a homology sphere $M_n(K_1,K_2)$ presented by two knots $K_1,K_2$ with linking number 1 and framing $(0,n)$. We call the manifold {\it Matsumoto's manifold}. We show that there exists no contractible bound of $M_n(T_{2,3},K_2)$ if $n<2τ(K_2)$ holds. We also give a formula of Ozsváth-Szabó's $τ$-invariant as…

We show that standard cyclic actions on Brieskorn homology 3-spheres with non-empty fixed set do not extend smoothly to any contractible smooth 4-manifold it may bound. The quotient of any such extension would be an acyclic $4$-manifold with boundary a related Brieskorn homology sphere. We briefly discuss well known in…

This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions. The property aspherical which is a purely homotopy theoretical condition implies…

Optimizes hybrid insurance contracts for heavy-tailed losses.

Kalshi prediction markets forecast cryptocurrency volatility through monetary policy and inflation signals.

We study the contribution of multiple covers of an irreducible rational curve C in a Calabi-Yau threefold Y to the genus 0 Gromov-Witten invariants in the following cases. (1) If the curve C has one node and satisfies a certain genericity condition, we prove that the contribution of multiple covers of degree d is given…

The article studies crystallizations of small covers over simple polytopes and finds unique crystallizations for the $n$-simplex.

In 1992, David Wright proved a remarkable theorem about which contractible open manifolds are covering spaces. He showed that if a one-ended open manifold M has pro-monomorphic fundamental group at infinity which is not pro-trivial and is not stably Z, then M does not cover any manifold (except itself). In the non-mani…

We show that every orientable 3-manifold is a classifying space BΓwhere Γis a groupoid of germs of homeomorphisms of R. This follows by showing that every orientable 3-manifold M admits a codimension one foliation F such that the holonomy cover of every leaf is contractible. The F we construct can be taken to be C^1 bu…

Consider the following distributed optimization scenario. A worker has access to training data that it uses to compute the gradients while a server decides when to stop iterative computation based on its target accuracy or delay constraints. The server receives all its information about the problem instance from the wo…

The paper explores coalescent contractions in contractible spaces, providing criteria and examples.

The study models life insurance policy cancellations using statistical and machine learning methods.

New insights into the structure of blown-up corona of hyperbolic groups.

The regular genus of certain 4-manifolds is determined, providing new insights.