Related papers: On the classification of topological defects and t…
Higher-order topological phases (HOTPs) hold gapped bulk bands and topological boundary states localized in boundaries with codimension higher than one. In this paper, we provide a unified construction and topological characterization of…
Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
This work discusses an approach to solving geometric construction problems in which the given figure is included in a set ordered by construction steps. The flow of information is carried through the chain, allowing the original problem to…
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe''…
In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…
Coupled layer constructions are a valuable tool for capturing the universal properties of certain interacting quantum phases of matter in terms of the simpler data that characterizes the underlying layers. In the study of fracton phases,…
We consider two categories related to symplectic manifolds: 1. Objects are symplectic manifolds and morphisms are symplectic embeddings. 2. Objects are symplectic manifolds endowed with compatible almost complex structure and morphisms are…
We describe a topological field theory that studies the moduli space of solutions of the symplectic vortex equations. It contains as special cases the topological sigma-model and topological Yang-Mills over Kahler surfaces. The correlation…
Iterated Segre mappings of real analytic generic submanifolds in complex space have been an essential tool in the study of holomorphic, formal, and CR mappings between such manifolds. In this paper we present a theory of iterated Segre…
A new technique is proposed to classify a topological field in abelian lattice gauge theories. We perform the classification by regarding the topological field as a local composite field of the gauge field tensor instead of the vector…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…
Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…
Gyromorphs are a new class of disordered systems that combine an amorphous-like absence of translational order with quasi-long-range rotational order. Gyromorphs can outperform quasicrystals or hyperuniform arrangements in forming isotropic…
Topological materials can host edge and corner states that are protected from disorder and material imperfections. In particular, the topological edge states of mechanical structures present unmatched opportunities for achieving robust…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…
We discuss the structure of topological defects in the context of extra dimensions where the symmetry breaking terms are localized. These defects develop structure in the extra dimension which differs from the case where symmetry breaking…
Determination of the symmetry property of superconducting gaps has been a central issue in studies to understand the mechanisms of unconventional superconductivity. Although it is often difficult to completely achieve the aforementioned…
Symmetry is one of the cornerstones of modern physics and has profound implications in different areas. In symmetry-protected topological systems, symmetries are responsible for protecting surface states, which are at the heart of the…