Related papers: Topological Surgery and its Dynamics

Stochastic processes are commonly used models to describe dynamics of a wide variety of nonequilibrium phenomena ranging from electrical transport to biological motion. The transition matrix describing a stochastic process can be regarded…

Exact string solutions are presented, where moduli fields are varying with time. They provide examples where a dynamical change of the topology of space is occurring. Some other solutions give cosmological examples where some dimensions are…

This paper initiates the study of topological arbiters, a concept rooted in Poincare-Lefschetz duality. Given an n-dimensional manifold W, a topological arbiter associates a value 0 or 1 to codimension zero submanifolds of W, subject to…

We prove that the canonical 4-dimensional surgery problems can be solved after passing to a double cover. This contrasts the long-standing conjecture about the validity of the topological surgery theorem for arbitrary fundamental groups…

We consider the problem of realizing tight contact structures on closed orientable three-manifolds. By applying the theorems of Hofer et al., one may deduce tightness from dynamical properties of (Reeb) flows transverse to the contact…

In the $\phi $-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between…

In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…

The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…

Topological defects are singularities within a field that cannot be removed by continuous transformations. The definition of these irregularities requires an ordered reference configuration, calling into question whether they exist in…

Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the {\em computationally dense\/} ones) are seen to be the ones…

We study the structure induced on a smooth manifold by a continuous selection of smooth functions. In case such selection is suitably generic, it provides a stratification of the manifold, whose strata are algebraically defined smooth…

We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators…

There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…

Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…

Multi-phase material are frequently applied in a wide variety of products, as they posses a unique set of properties by combining two or more distinct phases at the level of the microstructure. Although the macroscopic stiffness and…

We identify two rather novel types of (compound) dynamical bifurcations generated primarily by interactions of an invariant attracting submanifold with stable and unstable manifolds of hyperbolic fixed points. These bifurcation types -…

Topological defects play a central role in the physics of many materials, including magnets, superconductors and liquid crystals. In active fluids, defects become autonomous particles that spontaneously propel from internal active stresses…

In this paper we introduce a technique, called rim surgery, which can change a smooth embedding of an orientable surface of positive genus and nonnegative self-intersection in a smooth 4-manifold while leaving the topological embedding…

Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behavior of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable…