arXiv research

We give a complete description of all locally conformally Kähler structures with holomorphic Lee vector field on a compact complex manifold of Vaisman type. This provides in particular examples of such structures whose Lee vector field is not homothetic to the Lee vector field of a Vaisman structure. More generally, dr…

Study on Lee classes of complex surfaces, proving connectedness and bounds.

The Lee-Gauduchon cone is a convex cone of cohomology classes for complex manifolds.

Calculates knot $X$-torsion order using spectral sequences.

Calabi-Yau theorem extended to Vaisman manifolds.

New theorem on Lee classes for LCK manifolds with potential.

Butscher, D. Lee, Y. Lee, and Joyce constructed a special Lagrangian submanifold by gluing a Lawlor neck into a transverse intersection point of two special Lagrangian submanifolds. We prove a uniqueness theorem for the gluing of flat special Lagrangian tori of real dimension 3 in a flat complex torus of complex dimens…

Holomorphic tensors on Vaisman manifolds are invariant under the Lee field.

The paper studies LCAK metrics on complex manifolds and their properties.

We prove that the deRham cohomology classes of Lee forms of locally conformally symplectic structures taming the complex structure of a compact complex surface $S$ with first Betti number equal to $1$ is either a non-empty open subset of $H^1_{dR}(S, \mathbb R)$, or a single point. In the latter case, we show that $S$ …

In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.

We prove that a compact lcK manifold with holomorphic Lee vector field is Vaisman provided that either the Lee field has constant norm or the metric is Gauduchon (i.e., the Lee field is divergence-free). We also give examples of compact lcK manifolds with holomorphic Lee vector field which are not Vaisman.

The study examines Lee metrics on groups and their properties.

We prove that the Khovanov-Lee complex of an oriented link, L, in a thickened annulus, A x I, has the structure of a bifiltered complex whose filtered chain homotopy type is an invariant of the isotopy class of L in A x I. Using ideas of Ozsvath-Stipsicz-Szabo as reinterpreted by Livingston, we use this structure to de…

New insights on ACYT 6-manifolds reveal instanton conditions for curvature.

Synthetic proof of Gannon-Lee theorem for spacetimes.

Paper uses neural networks to calibrate Lee-Carter models for multiple populations.

Using the same method we provide negative answers to the following questions: Is it possible to find real equations for complex polynomials in two variables up to topological equivalence (Lee Rudolph) ? Can two topologically equivalent polynomials be connected by a continuous family of topologically equivalent polynomi…

We use a special kind of 2-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, in order to extend Khovanov homology from links to arbitrary tangles, not necessarily even. For every plane diagram of an oriented tangle, we construct a chain complex whose homology is invariant und…

Proves Gannon-Lee theorem for $C^1$ spacetimes.

We study the Euler-Lagrange equation for several natural functionals defined on a conformal class of almost Hermitian metrics, whose expression involves the Lee form $θ$ of the metric. We show that the Gauduchon metrics are the unique extremal metrics of the functional corresponding to the norm of the codifferential of…

New concept of $V$-minimality applied to Kaehler and non-Kaehler manifolds.

Lobb observed in [arXiv:1103.1412] that each equivariant sl(N) Khovanov-Rozansky homology over C[a] admits a standard decomposition of a simple form. In the present paper, we derive a formula for the corresponding Lee-Gornik spectral sequence in terms of this decomposition. Based on this formula, we give a simple alter…

This note is devoted to partial study of recurrent equation $dω=β\wedge ω$, based on linear algebra of exterior forms. Such equation was considered by Lee, for non-degenerate 2-form. In this note we approach general case, when $ω$ is arbitrary. Particularly, we extend results obtained by Lee, on odd-forms.

Study examines Weyl structures on Riemannian manifolds with vanishing Lee form.

We discuss a remarkable formula discovered by Jerison and Lee to classify constant scalar curvature pseudohermitian structures on the sphere. We show that the formula is valid in the wider context of Einstein pseudohermitian manifolds. As an application we prove a uniqueness result that generalizes the theorem of Jeris…

In this paper, we extend the classical Ho-Lee binomial term structure model to the case of time-dependent parameters and, as a result, resolve a drawback associated with the model. This is achieved with the introduction of a more flexible no-arbitrage condition in contrast to the one assumed in the Ho-Lee model.

We show that the page at which the Lee spectral sequence collapses gives a bound on the unknotting number, u(K). In particular, for knots with u(K)<3, we show that the Lee spectral sequence must collapse at the E_2 page. An immediate corollary is that the Knight Move Conjecture is true when u(K)<3.

We give a simple proof of Lee's result from [Adv. Math. 179 (2005) 554-586; arXiv:math.GT/0210213], that the dimension of the Lee variant of the Khovanov homology of a c-component link is 2^c, regardless of the number of crossings. Our method of proof is entirely local and hence we can state a Lee-type theorem for tang…

New link homology theories for $\mathbb{RP}^3$ yield distinct invariants.

In this article we use the combinatorial and geometric structure of manifolds with embedded cylinders in order to develop an adiabatic decomposition of the Hodge cohomology of these manifolds. We will on the one hand describe the adiabatic behaviour of spaces of harmonic forms by means of a certain Čech-de Rham complex…

Improved sample complexity for target Q-learning in finite MDPs with generative oracle.

Developed a new homology theory for graph chromatic polynomials.

We extend Bar-Natan's cobordism based categorification of the Jones polynomial to virtual links. Our topological complex allows a direct extension of the classical Khovanov complex ($h=t=0$), the variant of Lee ($h=0,t=1$) and other classical link homologies. We show that our construction allows, over rings of characte…

In this paper a multi-factor generalization of Ho-Lee model is proposed. In sharp contrast to the classical Ho-Lee, this generalization allows for those movements other than parallel shifts, while it still is described by a recombining tree, and is stationary to be compatible with principal component analysis. Based on…

Proves projectivity and ampleness of a Kähler manifold using complex Monge-Ampère equation.

Study shows torsion order bounds band-unlinking number for knot cobordisms.

Using certain solutions of the curve shortening flow, including self-shrinking and self-expanding curves or spirals, we construct and characterize many new examples of translating solitons for mean curvature flow in complex Euclidean plane. They generalize the Joyce, Lee and Tsui ones \cite{JLT} in dimension two. The s…

The exterior derivative $d θ$ of the Lee form $θ$ of almost Hermitian manifolds is studied. If $ω$ is the Kähler two-form, it is proved that the $\mathbb{R}ω$-component of $dθ$ is always zero. expressions for the other components, in $[λ_0^{1,1}]$ and in $[[ λ^{2,0} ]]$, of $dθ$ are also obtained. They are given in ter…

We introduce a class of hermitian metrics with {\em Lee potential}, that generalize the notion of l.c.K. metrics with potential introduced in \cite{ov} and show that in the classical examples of Calabi and Eckmann of complex structures on $S^{2p+1}\x S^{2q+1}$, the corresponding hermitian metrics are of this type. Thes…

Characterizes braid types and estimates twist coefficients.

Paper proves uniqueness of Einstein metrics on balls.

Researchers determine quantum filtration structure of torus links.

We study two kinds of transformation groups of a compact locally conformally Kahler (l.c.K.) manifold. First we study compact l.c.K. manifolds with parallel Lee form by means of the existence of a holomorphic l.c.K. flow. Next, we introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of diffeomorphisms pres…

This article applies a long short-term memory recurrent neural network to mortality rate forecasting. The model can be trained jointly on the mortality rate history of different countries, ages, and sexes. The RNN-based method seems to outperform the popular Lee-Carter model.

Regularities and stability shown for a specific type of complex parallelizable manifolds.

New invariants from divisibility of Lee classes for slice-torus.

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.