相关论文: Topology from the Bottom Up
Recent observations seem to indicate that we live in a universe whose spatial sections are nearly or exactly flat. Motivated by this we study the problem of observational detection of the topology of universes with flat spatial sections. We…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
The $s$-th higher topological complexity of a space $X$, $TC_s(X)$, can be estimated from above by homotopical methods, and from below by homological methods. We give a thorough analysis of the gap between such estimates when $X=RP^m$, the…
In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a…
Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The previous…
The lattice cohomology of a plumbed 3--manifold $M$ associated with a connected negative definite plumbing graph is an important tool in the study of topological properties of $M$, and in the comparison of the topological properties with…
We introduce cs-topologies, or topologies of open complemented subsets, as a new approach to constructive topology that preserves the duality between open and closed subsets of classical topology. Complemented subsets were used successfully…
Knowledge of the road network topology is crucial for autonomous planning and navigation. Yet, recovering such topology from a single image has only been explored in part. Furthermore, it needs to refer to the ground plane, where also the…
This paper revisits the origin of topology optimisation for fluid flow problems, namely the Poiseuille-based frictional resistance term used to parametrise regions of solid and fluid. The traditional model only works for true topology…
Topos theory occupies a singular place in contemporary mathematics: born from Grothendieck's algebraic geometry, it has emerged as a unifying language for geometry, topology, algebra, and logic. This book offers a progressive introduction…
We study the topology of singularities of $c$-optimal semicouplings in unequal dimension. Our main results describe homotopy-reductions from a source space $(X,\sigma)$ onto the singularities $Z_j$, $j\geq 0$ of $c$-optimal semicouplings…
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…
For analyzing stationary Yang-Mills connections in higher dimensions, one has to work with Morrey-Sobolev bundles and connections. The transition maps for a Morrey-Sobolev principal $G$-bundles are not continuous and thus the usual notion…
We show that bringing into proximity two topologically trivial systems can give rise to a topological phase. More specifically, we study a 1D metallic nanowire proximitized by a 2D superconducting substrate with a mixed s-wave and p-wave…
Engineering nanostructures from the bottom up enables the creation of carefully engineered complex structures that are not accessible via top down fabrication techniques, in particular, complex periodic structures for applications in…
We study $G_{2}$-manifolds obtained from circle bundles over symplectic $SU(3)$-manifolds with $T^{2}$-symmetry. When the geometry is multi-Hamiltonian, we show how the compact part of the resulting multi-moment graph for the…
Grand Unified Theories (GUTs) are a very well motivated extensions of the Standard Model (SM), but the landscape of models and possibilities is overwhelming, and different patterns can lead to rather distinct phenomenologies. In this work…
Basic concepts of higher local fields and topologies on their additive and multiplicative groups are introduced.
Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement…
In this work, major principles of the mathematical constitution of space and the principles of construction of the physical space are presented. Generalized conceptions of distances and dimensionality evaluation are proposed, together with…