arXiv research

New examples of variational bivectors found that are not Poissonian.

Covering space theory is used to construct new examples of buildings.

New topological biquandles created using skew braces.

A series of examples of toric Sasaki-Einstein 5-manifolds is constructed. These are submanifolds of toric 3-Sasaki 7-manifolds and such a Sasaki-Einstein 5-manifold corresponds uniquely to a toric 3-Sasaki 7-manifold. This produces examples of quasi-regular Sasaki-Einstein structures on every #k(S^2 xS^3), for k odd. T…

We present a new construction for obtaining pairs of higher-step isospectral Riemannian nilmanifolds and compare several resulting new examples. In particular, we present new examples of manifolds that are isospectral on functions, but not isospectral on one-forms.

Constructs examples of centrally harmonic spaces and shows they are not generically harmonic.

Raymond and Wiliams in "Examples of p-adic transformation groups", Ann. of Math. (2) 78 (1963) 92-106, constructed an action of the p-adic integers on an n-dimensional compactum, n>1, with the orbit space of dimension n+2. We present a simpler construction of such an example.

CleverHans is a software library that provides standardized reference implementations of adversarial example construction techniques and adversarial training. The library may be used to develop more robust machine learning models and to provide standardized benchmarks of models' performance in the adversarial setting. …

Constructs singular Yamabe solutions via equivariant reduction.

We describe a construction (the `warped cone construction') which produces examples of coarse spaces with large groups of translations. We show that by this construction we can obtain many examples of coarse spaces which do not have property A or which are not uniformly embeddable into Hilbert space.

New examples show scalar curvature's role in sphere stability.

Proves HNN extensions of nilpotent groups are left-orderable, constructs non-left-orderable examples.

We present simple new examples of pure-jump strict local martingales. The examples are constructed as exponentials of self-exciting affine Markov processes. We characterize the strict local martingale property of these processes by an integral criterion and by non-uniqueness of an associated ordinary differential equat…

Article is devoted to the Examples 2 and 3 of the symplectic solvable Lie groups $R$ with some special cohomological properties, which have been constructed by Benson and Gordon. But they are not succeeded in constructing corresponding compact forms for symplectic structures on these Lie groups. Recently A.Tralle prove…

We construct several non-trivial examples of CAT(1) spaces by using the idea of free construction.

We review the construction known as the Nahm transform in a generalized context, which includes all the examples of this construction already described in the literature. The Nahm transform for translation invariant instantons on $\real^4$ is presented in an uniform manner. We also analyze two new examples, the first o…

A twist construction for manifolds with torus action is described generalising certain T-duality examples and constructions in hypercomplex geometry. It is applied to complex, SKT, hypercomplex and HKT manifolds to construct compact simply-connected examples. In particular, we find hypercomplex manifolds that admit no …

New examples of structures found using twistor space.

New examples show clasp numbers can be zero yet four-genus can be arbitrarily large.

Review of recent G₂-structures on 7D manifolds.

We construct several new classes of isospectral manifolds with different local geometries. After reviewing a theorem by Carolyn Gordon on isospectral torus bundles and presenting certain useful specialized versions (Chapter 1) we apply these tools to construct the first examples of isospectral four-dimensional manifold…

Paper constructs new non-Anosov Partially Hyperbolic Geodesic flows using conformal deformations.

First non-trivial examples of deformed Spin(7)-instantons constructed.

Constructs stable bundles on K3 surfaces using monad construction.

We construct non-constructible simplicial $d$-spheres with $d+10$ vertices and non-constructible, non-realizable simplicial $d$-balls with $d+9$ vertices for $d\geq 3$.

New non-Kähler examples of generalized Kähler manifolds constructed via mapping tori.

We construct uncountably many simply connected open 3-manifolds with genus one ends homeomorphic to the Cantor set. Each constructed manifold has the property that any self homeomorphism of the manifold (which necessarily extends to a homeomorphism of the ends) fixes the ends pointwise. These manifolds are complements …

The study finds non-simple isotopy classes of links in 3-manifolds, including Legendrian and pseudo-Legendrian examples.

Hedlund constructed Riemannian metrics on n-tori, $n \geq 3$ for which minimal geodesics are very rare. In this paper we construct similar examples for every nilpotent fundamental group. These examples show that Bangert's existence results of minimal geodesics are optimal for nilpotent fundamental groups.

We construct examples of asymptotically cylindrical Riemannian 8-manifolds with holonomy group Spin(7). To our knowledge, these are the first such examples. The construction uses an extension to asymptotically cylindrical setting of Joyce's existence result for torsion-free Spin(7)-structures. One source of examples ar…

The study constructs geometrically decomposable aspherical 4-manifolds with non-zero signature and explores their properties.

We construct closed $(k-1)$-connected manifolds of dimensions $\ge 4k-1$ that possess non-trivial rational Massey triple products. We also construct examples of manifolds $M$ such that all the cup-products of elements of $H^k(M)$ vanish, while the group $H^{3k-1}(M;\Q)$ is generated by Massey products: such examples ar…

The paper constructs semistrict monoidal 2-categories from foam evaluations.

Bredon has constructed a 2-dimensional compact cohomology manifold which is not homologically locally connected, with respect to the singular homology. In the present paper we construct infinitely many such examples (which are in addition metrizable spaces) in all remaining dimensions $n \ge 3$.

In the article arXiv:1108.5443 we established a general group-theoretical approach to the construction of Bäcklund transformations. We then showed how this construction can be applied to construct Bäcklund transformation between equations which are Darboux integrable. Here we give a number of detailed examples and new …

New examples of harmonic unit vector fields on hyperbolic 3-space are constructed by exploiting the reduction of symmetry arising from the foliation by horospheres. This is compared and contrasted with the analogous construction in Euclidean 3-space, using a foliation by planes, which produces some new examples of harm…

We introduce a construction of pseudo-Anosov homeomorphisms on n-times punctured spheres and surfaces with higher genus using only sufficiently many positive half-twists. These constructions can produce explicit examples of pseudo-Anosov maps with various number-theoretic properties associated to the stretch factors, i…

Coassociative submanifolds are 4-dimensional calibrated submanifolds in $G_{2}$-manifolds. In this paper, we construct explicit examples of coassociative submanifolds in $Λ^{2}_{-} S^{4}$, which is the complete $G_{2}$-manifold constructed by Bryant and Salamon. Classifying the Lie groups which have 3- or 4-dimensional…

In this paper we generalize examples of Hamiltonian stationary Lagrangian submanifolds constructed by Lee and Wang in $\mathbb{C}^m$ to toric almost Calabi-Yau manifolds. We construct examples of weighted Hamiltonian stationary Lagrangian submanifolds in toric almost Calabi-Yau manifolds and solutions of generalized La…

We construct explicit examples of Dirac-harmonic maps $(φ, ψ)$ between Riemannian manifolds $(M,g)$ and $(N,g')$ which are non-trivial in the sense that $φ$ is not harmonic. When $\dim M=2$, we also produce examples where $φ$ is harmonic, but not conformal, and $ψ$ is non-trivial.

In this paper, we consider new components of the key space of the Moduli space of minimal surfaces in flat 4-tori and calculate their dimensions. Moreover, we construct an example of minimal surfaces in 4-tori and obtain an element of the Moduli. In the process of the construction, we give an example of minimal surface…

I point out some very elementary examples of special Lagrangian tori in certain Calabi-Yau manifolds that occur as hypersurfaces in complex projective space. All of these are constructed as real slices of smooth hypersurfaces defined over the reals. This method of constructing special Lagrangian submanifolds is well kn…

We discuss the construction of Sp(2)Sp(1)-structures whose fundamental form is closed. In particular, we find 10 new examples of 8-dimensional nilmanifolds that admit an invariant closed 4-form with stabiliser Sp(2)Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We present a thorough inve…

Finding examples of tangentially degenerate submanifolds (submanifolds with degenerate Gauss mappings) in an Euclidean space $R^4$ that are noncylindrical and without singularities is an important problem of differential geometry. The first example of such a hypersurface was constructed by Sacksteder in 1960. In 1995 W…

We construct new examples of self-similar solutions and translating solitons for Lagrangian mean curvature flow by extending the method of Joyce, Lee and Tsui. Those examples include examples in which the Lagrangian angle is arbitrarily small as the examples of Joyce, Lee and Tsui.

In this paper, we construct various examples of Lagrangian mean curvature flows in Calabi-Yau manifolds, using moment maps for actions of abelian Lie groups on them. The examples include Lagrangian self-shrinkers and translating solitons in the Euclidean spaces. Moreover, our method can be applied to construct examples…

Working with group homomorphisms, a construction of manifolds is introduced to preserve homology groups. The construction gives as special cases Qullien's plus construction with handles obtained by Hausmann, the existence of one-sided $h$-cobordism of Guilbault and Tinsley, the existence of homology spheres and higher-…

In this paper we present a construction of stable bundles on Calabi-Yau threefolds using the method of bundle extensions. This construction applies to any given Calabi-Yau threefold with h^{1,1}>1. We give examples of stable bundles of rank 2 and 4 constructed out of pure geometric data of the given Calabi-Yau space. A…