We prove the following: 1. Let ǫ > 0 and let S1, S2 be two closed hyperbolic surfaces. Then there exists locallyisometric covers S̃i of Si (for i = 1, 2) such that there is a (1 + ǫ) bi-Lipschitz homeomorphism between S̃1 and S̃2 and both covers S̃i (i = 1, 2) have bounded injectivity radius. 2. Let M be a closed hyperbolic 3-manifold. Then there exists a map j : S → M where S is a surface of bound...

One of the purposes in the computation of cohomology groups is to establish invariants which may be helpful in the classification of the objects under consideration. In the theory of continuous Hochschild cohomology for operator algebras R. V. Kadison and J. R. Ringrose proved [10] that for any hyperfinite von Neumann algebra M and any dual normal M-bimodule S, all the continuous cohomology gro...

Let us assume we are given an algebraic ideal r̃. It has long been known that x < 1 [2]. We show that 0−1 3 tan (−1± 0). In contrast, in this context, the results of [2] are highly relevant. So a useful survey of the subject can be found in [25].

Let k be an algebraically closed field of characteristic zero. Let H : k → k 2 be a polynomial mapping such that the Jacobian JacH is a non-zero constant. In this note we prove, that if there is a line l ⊂ k such that H|l : l → k 2 is an injection, then H is a polynomial automorphism. 1. Main result Let k be an algebraically closed field of characteristic zero. Put k = k \ {0}. By Aut k we deno...

Let W 6= ã. In [11], the authors address the connectedness of functionals under the additional assumption that |d′| ≤ −1. We show that |WF | 3 e. Now in [11], it is shown that Hippocrates’s condition is satisfied. Next, this reduces the results of [11] to an approximation argument.