Related papers: Tight and overtwisted contact structures
This is an article on the interaction between topology and physics which will appear in 1998 in a book called: A History of Topology, edited by Ioan James and published by Elsevier-North Holland.
A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises from this definition. Many plausible results follow from this…
In this article, we answer-for a class of magnetic systems-a question now known as the contact type conjecture, whose origin trace back to the 1998 work of Contreras, Iturriaga, Paternain, and Paternain. For a broad class of magnetic…
In this article we classify up to isotopy tight contact structures on Seifert manifolds over the torus with one singular fibre.
In this article we provide an infinite family of weakly symplectically fillable contact structures with trivial Ozsvath-Szabo contact invariants over Z/2Z. As a consequence of this fact, we show how Heegaard-Floer theory can distinguish…
Previous study of contact of power-law graded materials concerned the contact of a rigid body (punch) with an elastic inhomogeneous foundation whose inhomogeneity is characterized by the Young modulus varying with depth as a power function.…
We study some properties of transverse contact structures on small Seifert manifolds, and we apply them to the classification of tight contact structures on a family of small Seifert manifolds.
Bourgeois proved in [5] that odd-dimensional tori admit a contact structure. We shall prove a more general result: Any odd-dimensional parallelisable closed manifold admits a contact structure. This implies that a solvmanifold $\Gamma…
This paper presents a new proof of the Giroux Correspondence for tight contact $3$-manifolds using techniques from Heegaard splittings and convex surface theory. We introduce tight Heegaard splittings, which generalise the Heegaard…
We employ cut and paste contact topological techniques to classify some tight contact structures on the closed, oriented genus-2 surface times the interval. A boundary condition is specified so that the Euler class of the of the contact…
In this note we observe that while all overtwisted contact structures on compact 3--manifolds are supported by planar open book decompositions, not all contact structures are. This has relevance to invariants of contact structures and also…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
Symmetry plays a key role in determining the physical properties of materials. By Neumann's principle, the properties of a material are invariant under the symmetry operations of the space group to which the material belongs. Continuous…
In this document we present a twistor correspondence for half-flat almost-Grassmannian structures on real and complex manifolds. We provide foundational results regarding local theory in the complex setting and a global correspondence when…
The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…
We show the existence of elements of infinite order in some homotopy groups of the contactomorphism group of overtwisted spheres. It follows in particular that the contactomorphism group of some high dimensional overtwisted spheres is not…
In Persson's seminal work on tire-road interaction (Persson, J. Chem. Phys. {\bf 115}(8), 2001), he ingeniously derived a diffusion equation in Appendix B to characterize the evolution of contact pressure between a rigid rough indenter and…
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…
The classic Johnson Kendall Roberts (JKR) theory describes the short-ranged adhesive contact of elastic bodies, but is only valid for axisymmetric contact. A theory for non-axisymmetric contact, which relies on approximating the contact…
We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent bundles, ${\rm…