We define topological and analytic indices in R/Z K-theory and show that they are equal.

The problem of reassembling an object from its parts or fragments has never been addressed with a unified computational approach, which depends on the pure geometric form of the parts and not application-specific features. We propose a method for the automatic reconstruction of a model based on the geometry of its parts, which may be computergenerated models or range-scanned models. The matchin...

Let p be a prime number. In this article we present a theorem, suggested by Peter Scholze, which states that Gal(Qp/Qp) is the étale fundamental group of a certain object Z which is defined over an algebraically closed field. This object is the quotient of the “punctured perfectoid open disk” by an action of the group Qp . The proof of this fact combines two themes: the tilting equivalence for ...

The use of Geometric Logic as the foundation of a speciication language called GeoZ is proposed elsewhere 4]. In this note we explore GeoZ from the perspective of practitioners, who are familiar with the existing Z notation, by explaining the issues that arise and the essential role of schema entailment in the GeoZ reformulation of Z's mathematical toolkit.

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...