Related papers: Linking, Legendrian linking and causality

We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are wrong when…

In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alternative proof of a theorem concerning a relationship…

A unifying framework for the study of causal relations is presented. The causal relations are regarded as subsets of M x M and the role of the corresponding antisymmetry conditions in the construction of the causal ladder is stressed. The…

Let $\Lambda, \Lambda'$ be a pair of closed Legendrian submanifolds in a closed contact manifold $(Y, \xi = Ker(\alpha))$ related by a Legendrian cobordism $W\subset (\mathbb{C}\times Y, \tilde{\xi}=Ker(-y dx +\alpha))$. In this note, we…

Given a real analytic function $f$ from $\mathbb{R}^4$ to $\mathbb{R}^2$ with isolated critical point at the origin, the link $L_f$ of the singularity is a real fibred knot in $\mathbb{S}^{3}$. From this singularities, we construct a family…

Let $\mathcal{E}^3\subset TM^n$ be a smooth $3$-distribution on a smooth manifold of dimension $n$ and $\mathcal{W}\subset\mathcal{E}$ a line field such that $[\mathcal{W},\mathcal{E}]\subset\mathcal{E}$. Under some orientability…

We define a differential graded algebra associated to Legendrian knots in Seifert fibered spaces with transverse contact structures. This construction is distinguished from other combinatorial realizations of contact homology invariants by…

A central property of a classical geometry is that the geodesic distance between two events is \emph{additive}. When considering quantum fluctuations in the metric or a quantum or statistical superposition of different spacetimes,…

For any Legendrian knot or link in $\mathbb{R}^3$, we construct an $L_\infty$ algebra that can be viewed as an extension of the Chekanov-Eliashberg differential graded algebra. The $L_\infty$ structure incorporates information from rational…

In this conference published in 1997 some problems on the geodesics of a Lorentzian manifold concerning causality and infinite-dimensional variational methods, are pointed out. Even though a big progress on many of these questions have been…

In this paper we prove that every open Riemann surface properly embeds in the Special Linear group $SL_2(\mathbb{C})$ as a holomorphic Legendrian curve, where $SL_2(\mathbb{C})$ is endowed with its standard contact structure. As a…

The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…

Often it is possible to equip the space of all cone geodesics of a strongly convex cone structure with the structure of a smooth contact manifold. This generalizes the analogous notions for the space of light rays of a Lorentzian spacetime.…

A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal…

Suppose that L is a null--homologous Legendrian knot in a contact 3--manifold. We determine the connection between the sutured invariant of the complement of L and the Legendrian invariant defined by Lisca, Ozsvath, Stipsicz and Szabo. In…

This article proves hypersurfaces of degree d in projective n-space are "rationally simply-connected" if $d^2 \leq n$. In a forthcoming paper, de Jong and I prove a slightly weaker result when $d^2 \leq n+1$.

We study the interplays between paracontact geometry and the theory of bi-Legendrian manifolds. We interpret the bi-Legendrian connection of a bi-Legendrian manifold M as the paracontact connection of a canonical paracontact structure…

We introduce a canonical, compact topology, which we call weakly causal, naturally generated by the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by certain problems of quantum gravity. We show…

It is shown that, in the 1-jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component of the links considered is legendrian…

For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to…