We prove that an iterated torus knot type fails the uniform thickness property (UTP) if and only if all of its iterations are positive cablings, which is precisely when an iterated torus knot type supports the standard contact structure. We also show that all iterated torus knots that fail the UTP support cabling knot types that are transversally non-simple.

We formulate a fictitious-time flow equation which drives an initial guess torus to a torus invariant under given dynamics, provided such torus exists. The method is general and applies in principle to continuous time flows and discrete time maps in arbitrary dimension, and to both Hamiltonian and dissipative systems.

Each closed oriented 3-manifoldM is naturally associated with a set of integersD(M), the degrees of all self-maps on M . D(M) is determined for each torus bundle and torus semi-bundle M . The structure of torus semi-bundle is studied in detail. The paper is a part of a project to determine D(M) for all 3-manifolds in Thurston’s picture.

We discuss BFV deformation quantization [5] in the special case of a linear Hamiltonian torus action. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of [2] for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.

We define periodic frameworks as graphs on the torus, using the language of gain graphs. We present some fundamental definitions and results about the infinitesimal rigidity of graphs on a torus of fixed size and shape, and find necessary conditions for the generic rigidity of periodic frameworks on a d-dimensional fixed torus.

Conic sections embedded in a torus must be circles of special types: (i) proole circles, (ii) cross-sectional circles , and (iii) Yvone-Villarceau circles. Based on this classiication, we present eecient and robust geometric algorithms that detect and compute all degenerate conic sections (circles) in torus/plane and torus/natural-quadric intersections. 2 Introduction Simple surfaces (such as p...

We study how axisymmetric magnetohydrodynamical (MHD) accretion flows depend on γ adiabatic index in the polytropic equation of state. This work is an extension of Mościbrodzka & Proga (2008), where we investigated the γ dependence of 2-D Bondilike accretion flows in the hydrodynamical (HD) limit. Our main goal is to study if simulations for various γ can give us insights into to the problem of...

The 'simplest' entanglements of the graph of edges of the cube are enumerated, forming two-cell {6, 3} (hexagonal mesh) complexes on the genus-one two-dimensional torus. Five chiral pairs of knotted graphs are found. The examples contain non-trivial knotted and/or linked subgraphs [(2, 2), (2, 4) torus links and (3, 2), (4, 3) torus knots].

We establish conditions for distinguishing between two topologically identical strange attractors that are enclosed by identical bounding tori, one of which is generated by a flow restricted to that torus, the other of which is generated by a flow in a different bounding torus and either imaged or lifted into the first bounding torus.

We discuss a clumpy model of obscuring dusty tori around AGN. Cloudcloud collisions lead to an effective viscosity and a geometrically thick accretion disk, which has the required properties of a torus. Accretion in the combined gravitational potential of central black hole and stellar cluster generates free energy, which is dissipated in collisions, and maintains the thickness of the torus. A ...