Related papers: Physics on manifolds with exotic differential stru…
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
In continuum physics, there are important topological aspects like instantons, theta-terms and the axial anomaly. Conventional lattice discretizations often have difficulties in treating one or the other of these aspects. In this paper, we…
We produce examples of pairwise non-diffeomorphic closed irreducible 4-manifolds with non-trivial free abelian fundamental group of rank less than three and small Euler characteristic. These exotic smooth structures become standard after…
We establish the existence of a pair of exotic surfaces in a punctured $K3$ which remains exotic after one external stabilization and have diffeomorphic complements. A key ingredient in the proof is a vanishing theorem of the family…
We construct supersymmetric gauge theories on some curved manifolds with boundaries. Our examples include a part of three-sphere and a part of two-sphere. We concentrate on Dirichlet boundary conditions. For these theories on the manifolds…
Topological surface states with intrinsic magnetic ordering in the MnBi$_2$Te$_4$(Bi$_2$Te$_3$)$_n$ compounds have been predicted to host rich topological phenomena including quantized anomalous Hall effect and axion insulator state. Here…
The theory of intersection spaces assigns cell complexes to certain stratified topological pseudomanifolds depending on a perversity function in the sense of intersection homology. The main property of the intersection spaces is Poincar\'e…
It is shown that the geometry of parallelizable manifolds can be extended to non-parallelizable ones by extending the connection that a global frame field would define on a parallelizable manifold to a connection that a singular frame field…
Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$,…
We use differential cohomology to systematically construct a large class of topological actions in physics, including Chern-Simons terms, Wess-Zumino-Novikov-Witten terms, and theta terms (continuous or discrete). We introduce a notion of…
The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the…
This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence…
We shall give a twisted Dirac structure on the space of irreducible connections on a SU(n)-bundle over a three-manifold, and give a family of twisted Dirac structures on the space of irreducible connections on the trivial SU(n)-bundle over…
We prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire-Milnor invariant for surfaces and we give a…
Most nonabelian gauge theories admit the existence of conserved and quantized topological charges as generalizations of the Dirac monopole. Their interactions are dictated by topology. In this paper, previous work in deriving classical…
The energy-momentum relationship of electrons on the surface of an ideal "Hydrogen-Atom" Topological Insulator forms a cone - a Dirac cone, which, when warped and distorted (no longer described by the Dirac equation), can lead to unusual…
In accordance with recent progress of fracton topological phases, unusual topological phases of matter hosting fractionalized quasiparticle excitations with mobility constraints, new type of symmetry is studied -- multipole symmetry,…
We consider monopoles with singularities of Dirac type on quasiregular Sasakian three-folds fibering over a compact Riemann surface $\Sigma$, for example the Hopf fibration $S^3\longrightarrow S^2$. We show that these correspond to…
We try to convince the reader that the categorical version of differential geometry, called Synthetic Differential Geometry (SDG), offers valuable tools which can be applied to work with some unsolved problems of general relativity. We do…