Pursuit Nontrivial

Every Nontrivial Knot in S Has Nontrivial A-polynomial

We show that every nontrivial knot in the 3-sphere has a nontrivial A-polynomial. In Theorem 1 of [3], Kronheimer and Mrowka give a proof of the following remarkable theorem, thereby establishing the truth of the Property P conjecture. Theorem 0.1 (Kronheimer-Mrowka). Let K be any nontrivial knot in S and let M(r) be the manifold obtained by Dehn surgery on K with slope r with respect to the st...

Nontrivial spontaneous synchronization.

The collective behavior of an ensemble of multimode stochastic oscillators is investigated. The oscillators are pulse coupled; they are able to emit pulses and to detect the pulses emitted by the others. As a function of the output intensity in the system they can operate in different modes having different pulsing periods. The system is designed to optimize the output intensity around a fixed ...

Ogy with Nontrivial Topology

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with negative spatial curvature.

Forced Topological Nontrivial Field Configurations

The motion of a one-dimensional kink and its energy losses are considered as a model of interaction of nontrivial topological field configurations with external fields. The approach is based on the calculation of the zero modes excitation probability in the external field. We study in the same way the interaction of the t’Hooft–Polyakov monopole with weak external fields. The basic idea is to t...

On Nontrivial Approximation of CSPs