Related papers: Trace Maps on Rigid Stein Spaces
Previous symmetry-based database searches have already revealed ubiquitous band topology in nature, while the destiny of band topology under symmetry-breaking is yet to be studied comprehensively. Here we first develop a framework allowing…
We define a tracelike transformation to be a natural family of conjugation invariant maps $T_{x,C}: hom_C(x,x) \to hom_C(1,1)$ for all dualisable objects $x$ in any symmetric monoidal infinity-category $C$. This generalises the trace from…
Given a code from a shift space to an irreducible sofic shift, any two of the following three conditions -- open, constant-to-one, (right or left) closing -- imply the third. If the range is not sofic, then the same result holds when…
We extend Stone duality between generalized Boolean algebras and Boolean spaces, which are the zero-dimensional locally-compact Hausdorff spaces, to a non-commutative setting. We first show that the category of right-handed skew Boolean…
In this article we give a homological characterization of the topology of Stein spaces over any valued base field. In particular, when working over the field of complex numbers, we obtain a characterization of the usual Euclidean…
For a group $G$, we construct a quasi morphism from its left orderings and the map from the space of left orderings to the second bounded cohomology. We show that these maps reflect various properties of the group orderings.
Under the application of a force, a material will deform and, hence, the crystal lattice will experience strain. This induced strain will alter the electronic properties of the material. In particular, strain in graphene generates an…
We establish the invariant trace formula (\`a la Arthur) for the ad\'elic covers of connected reductive groups over a number field, under the hypothesis that the trace Paley-Wiener theorem is verified for all Levi subgroups at the real…
We develop a generalized field space geometry for higher-derivative scalar field theories, expressing scattering amplitudes in terms of a covariant geometry on the all-order jet bundle. The incorporation of spacetime and field derivative…
We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the…
We revisit sigma models on target spaces given by a principal torus fibration $X\to M$, and show how treating the 2-form B as a gerbe connection captures the gauging obstructions and the global constraints on the T-duality. We show that a…
In the present paper, we devise a version of topological $L^2$-Serre duality for singular complex spaces with arbitrary singularities. This duality is used to deduce various new $L^2$-vanishing theorems for the $\bar{\partial}$-equation on…
We investigate when a commutative ring spectrum $R$ satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to do this, we prove an ascent theorem for local Gorenstein…
A map $f:X\to Y$ between topological spaces is defined to be {\em scatteredly continuous} if for each subspace $A\subset X$ the restriction $f|A$ has a point of continuity. We show that for a function $f:X\to Y$ from a perfectly paracompact…
This paper studies the connection between the quantum trace map -- which maps the $\mathfrak{sl}_2$-skein module to the quantum Teichm\"uller space for surfaces and to the quantum gluing module for 3-manifolds -- and the quantum UV-IR map…
In this article we study two "strong" topologies for spaces of smooth functions from a finite-dimensional manifold to a (possibly infinite-dimensional) manifold modeled on a locally convex space. Namely, we construct Whitney type topologies…
We prove that a Lebesgue measure-preserving linked-twist map defined in the plane is metrically isomorphic to a Bernoulli shift (and thus strongly mixing). This is the first such result for an explicitly defined linked-twist map on a…
We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has a continuous or homeomorphic extension to the closures of the domains. Our conditions involve the…
We investigate the combinatorial and dynamical properties of so-called nearly Euclidean Thurston maps, or NET maps. These maps are perturbations of many-to-one folding maps of an affine two-sphere to itself. The close relationship between…
We discuss various known generalizations of the classical Hartogs' extension theorem on Stein spaces with arbitrary singularities and present an analytic proof based on d-bar methods.