The purpose of this note is to use covering space theory to construct new examples of buildings. On the level of Coxeter systems, this contsruction was described previously in Davis [4]. It goes as follows. Start with a Coxeter system (W ′, S). Change some m(s, t)’s in its Coxeter matrix from integers ≥ 2 to the symbol ∞ . This defines a new Coxeter system (W, S). Suppose C′ is a building of ty...

This article contains a new argument which proves vanishing of the first cohomology for negative vector bundles over a complex projective variety if the rank of the bundle is smaller than the dimension of the base. Similar argument is applied to the construction of holomorphic functions on the universal covering of the complex projective variety .

This paper describes certain properties of the fundamental group of the shrinking wedge of circles. Covering space theory is an inadequate tool since the shrinking wedge of circles is not semi-locally simply connected. We conclude with the fact that the shrinking wedge of circles is not homotopy equivalent to the wedge product of a countable number of circles.

For a holomorphic one-form $${\xi }$$ on weakly 1-complete manifold X with certain properties, we will discuss the connectivity of pair $$(\hat{X},F^{-1}(z))$$ , where $$\pi :\hat{X} \rightarrow X$$ is covering map and F function $$\hat{X}$$ such that $$dF=\pi ^*{\xi . We also criteria about when admits proper mapping onto Riemann surface.

A natural and practical criterion in the preparation of diagrams of ordered sets is to minimize the number of different slopes used for the edges. Any diagram requires at least the maximum number of upper covers (or of lower covers) of any element. While this maximum degree is not always enough we show that it is as long as any edge joining a covering pair may be bent, to produce a crooked diag...

Does leaving a currency union reduce international trade? We answer this question using a large annual panel data set covering 217 countries from 1948 through 1997. During this sample a large number of countries left currency unions; they experienced economically and statistically significant declines in bilateral trade, after accounting for other factors. Assuming symmetry, we estimate that a ...

Data-intensive Grid applications need access to large datasets that may each be replicated on different resources. Minimizing the overhead of transferring these datasets to the resources where the applications are executed requires that appropriate computational and data resources be selected. In this paper, we introduce a heuristic for the selection of resources based on a solution to the Set ...

In this paper we give an explicit and constructive description of the pairs (p. A) of elements in the symmetric group S, which can be realized as the image of the meridian-longitude pair of some knot K in the 3-sphere S3 under a representation xi (S’ K) -t S,,. The result is applied to give an otherwise nonobvious restriction on the numbers of branch curves of a branched covering , of S’, answe...

Given a finite Weyl group W with root system , assign the weight α ∈ to each covering pair in the Bruhat order related by the reflection corresponding to α. Extending this multiplicatively to chains, we prove that the sum of the weights of all maximal chains in the Bruhat order has an explicit product formula, and prove a similar result for a weighted sum over maximal chains in the Bruhat order...

Does leaving a currency union reduce international trade? We answer this question using a large annual panel data set covering 217 countries from 1948 through 1997. During this sample a large number of countries left currency unions; they experienced economically and statistically significant declines in bilateral trade, after accounting for other factors. Assuming symmetry, we estimate that a ...