Related papers: On the future cover of a sofic shift
The paper describes a cover of the future cover of a sofic shift which is canonical in the same way as the future cover itself. In some cases the cover is isomorphic to the future cover and in other it is a genuine extension.
A canonical cover generalizing the left Fischer cover to arbitrary sofic shifts is introduced and used to prove that the left Krieger cover and the past set cover of a sofic shift can be divided into natural layers. These results are used…
The flow equivalence of sofic shifts is examined using results about the structure of the corresponding covers. A canonical cover generalising the left Fischer cover to arbitrary sofic shifts is introduced and used to prove that the left…
We prove that the Karoubi envelope of a shift --- defined as the Karoubi envelope of the syntactic semigroup of the language of blocks of the shift --- is, up to natural equivalence of categories, an invariant of flow equivalence. More…
In this paper, we introduce a new canonical connection on Riemannian manifold with a distribution. Moreover, as an application of the connection, we give a geometric proof of the Frobenius theorem.
A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds which were proposed in the last decades. Such an operation is indispensable in order to perform…
The covering radius of a shift space is a quantity of interest for information-theoretic applications of data transmission over noisy channels. We prove that the covering radius of a primitive sofic shift is a rational number, and describe…
We prove a generalized version of Kazhdan's theorem for canonical forms on Riemann surfaces. In the classical version, one starts with an ascending sequence $\{S_n \rightarrow S\}$ of finite Galois covers of a hyperbolic Riemann Surface…
We develop the theory of Schur covers of finite skew braces. We prove the existence of at least one Schur cover. We also compute several examples. We prove that different Schur covers are isoclinic. Finally, we prove that Schur covers have…
Let f be a generically finite morphism from X to Y. The purpose of this paper is to show how the O_Y algebra structure on the push forward of O_X controls algebro-geometric aspects of X like the ring generation of graded rings associated to…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
Topos properties of the category of covering groupoids over a fixed groupoid are discussed. A classification result for connected covering groupoids over a fixed groupoid analogous to the fundamental theorem of Galois theory is given.
This note concerns exponential sheaves and the "universal" Fourier transform on them. Fourier invertibility and the subsequent Fourier miracle is demonstrated. Further, t-structures and realizations are constructed and shown to have…
The purpose of this note is to establish, in a categorical manner, the universality of the Geroch-Kronheimer-Penrose causal boundary when considering the types of causal structures that may profitably be put on any sort of boundary for a…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
The paper is partly a survey with historical background and references, partly provides the opportunity to put in print some unpublished early work, and partly has new results. A special case of relative categoricity is identified (almost…
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
A method is presented for imputing a topology for any chronological set, i.e., a set with a chronology relation, such as a spacetime or a spacetime with some sort of boundary. This topology is shown to have several good properties, such as…
In this paper we will present a proof of the consistency of Quine's set theory "New Foundations" (hereinafter NF), so-called after the title of the 1937 paper in which it was introduced. This version takes the approach of building a model…
We present an improved version of the cyclic covering trick, which works inside the category of toroidal embeddings