Related papers: Does Zeeman's Fine Topology Exist?
We set an upper bound on the gravitational cutoff in theories with exact quantum numbers of large N periodicity, such as Z_N discrete symmetries. The bound stems from black hole physics. It is similar to the bound appearing in theories with…
We further sharpen higher type adjunction inequalities of P. Ozsv\'ath and Z. Szab\'o on a 4-manifold $M$ with a nonzero Seiberg-Witten invariant for a Spin$^c$ structure $\frak{s}$, when an embedded surface $\Sigma\subset M$ satisfies…
In this paper it is stressed that there is no {\em physical} reason for symmetries to be linear and that Lie group theory is therefore too restrictive. We illustrate this with some simple examples. Then we give a readable review on the…
The cross topology $\gamma$ on a product of topological spaces $X$ and $Y$ is the collection of all sets $G\subseteq X\times Y$ such that the intersection of $G$ with every vertical line and every horizontal line is an open subset of either…
We solve a super Toda system on a closed Riemann surface of genus~$\gamma>1$ and with some particular spin structures. This generalizes the min-max methods and results for super Liouville equations and gives new existence results for super…
Modifying a construction of W. Marciszewski we prove (in ZFC) that there exists a subspace of the real line $\mathbb{R}$, such that the realcompact space $C_p(X)$ of continuous real-valued functions on $X$ with the pointwise convergence…
We investigate suitable, physically motivated conditions on spacetimes containing certain submanifolds - the so-called {weakly trapped submanifolds} - that ensure, in a set of neighboring metrics with respect to a convenient topology, that…
Let $M$ be a complete, connected Riemannian surface and suppose that $\mathcal{S} \subset M$ is a discrete subset. What can we learn about $M$ from the knowledge of all distances in the surface between pairs of points of $\mathcal{S}$? We…
The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike…
As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open…
We consider shape optimization problems for elasticity systems in architecture. A typical question in this context is to identify a structure of maximal stability close to an initially proposed one. We show the existence of such an…
A $\sigma$-frame is a poset with countable joins and finite meets in which binary meets distribute over countable joins. The aim of this paper is to show that $\sigma$-frames, actually $\sigma$-locales, can be seen as a branch of Formal…
The equations of motion and the Bianchi identity of the C-field in M-theory are encoded in terms of the signature operator. We then reformulate the topological part of the action in M-theory using the signature, which leads to connections…
We prove Zimmer's conjecture for $C^2$ actions by finite-index subgroups of $\mathrm{SL}(m,\mathbb{Z})$ provided $m>3$. The method utilizes many ingredients from our earlier proof of the conjecture for actions by cocompact lattices in…
The recent developments in the study of topological multi-boundary entanglement in the context of 3d Chern-Simons theory (with gauge group $G$ and level $k$) suggest a strong interplay between entanglement measures and number theory. The…
In the present paper we study necessary and sufficient conditions for the existence of a semicontinuous and finite Richter-Peleg multi-utility for a preorder. It is well know that, given a preorder on a topological space, if there is a…
The unitarity of the 4D lattice theory of gravity in the case of the Minkowski signature is proved. The proof is valid only for lattices that conserve the number of degrees of freedom during time evolution. The Euclidean signature and the…
We discuss self-similar solutions to $O(4)$ textures in Minkowski space and in flat Friedmann-Robertson-Walker backgrounds. We show that in the Minkowski case there exist no solutions with winding number greater than unity. However, we find…
I review the study of real (Minkowski) time correlators in hot, weakly coupled Yang-Mills theory via lattice methods. I concentrate on the Minkowski time topological susceptibility, which is related to the efficiency of baryon number…
We construct stable minimal hypersurfaces with simple topology in certain compact $4$-manifolds $X$ with boundary, where $X$ embeds into a smooth manifold homeomorphic to $S^4$. For example, if $X$ is equipped with a Riemannian metric $g$…