We exhibit new examples of double Kodaira fibrations by using finite Galois covers a product $\Sigma_b \times \Sigma_b$, where $\Sigma_b$ is smooth projective curve genus $b \geq 2$. Each cover obtained providing an explicit group epimorphism from the pure braid $\mathsf{P}_2(\Sigma_b)$ to some Heisenberg group. In this way, we are able show that every $b$ base fibration; moreover, number pairw...

‎There is a flatness property of acts over monoids called Condition $(PWP)$ which‎, ‎so far‎, ‎has received‎ ‎much attention‎. ‎In this paper‎, ‎we introduce Condition GP-$(P)$‎, ‎which is a generalization of Condition $(PWP)$‎. ‎Firstly‎, ‎some  characterizations of monoids by Condition GP-$(P)$ of their‎ ‎(cyclic‎, ‎Rees factor) acts are given‎, ‎and many known results are generalized‎. ‎More...

ABSTRACT. Torsion and Betti numbers for knots are special cases of more general invariants br and βr, respectively, associated to a finitely generated group G and epimorphism χ : G → Z. The sequence of Betti numbers is always periodic; under mild hypotheses about (G,χ), the sequence br satisfies a linear homogeneous recurrence relation with constant coefficients. Generally, br exhibits exponent...

Abstract Let G be a finitely generated group that can written as an extension $$ \begin{align*} 1 \longrightarrow K \stackrel{i}{\longrightarrow} \stackrel{f}{\longrightarrow} \Gamma \end{align*} where is group. By study of the Bieri–Neumann–Strebel (BNS) invariants we prove if $b_1(G)> b_1(\Gamma ) > 0$ , then algebraically fibres; is, admits epimorphism to $\Bbb {Z}$ with kernel. An int...

Let G be a connected real Lie group. The universal representation kernel, Ko, oí G is defined as the intersection of all kernels of continuous finite dimensional representations of G. Evidently, Ko is a closed normal subgroup of G, and it is known from a theorem due to Goto (cf. [l, Theorem 7.1]) that G/Ko has a faithful continuous finite dimensional representation. Thus Kg is the smallest norm...

This note gives a complete characterization of when the ordinal sum of two lattices (the lattice obtained by placing the second lattice on top of the first) is projective. This characterization applies not only to the class of all lattices, but to any variety of lattices, and in particular, to the class of distributive lattices. Lattices L with the property that every epimorphism onto L has an ...

Here we investigate algebras associated with algebraizations of (variants of) first-order logic and of multi-modal logics. We will use the notation of the fundamental textbook Henkin Monk Tarski [8] (Parts I, II) of algebraic logic, but we will try to keep the present note self-contained. In a way, this work is a continuation of [23] but we do not assume familiarity with that work. For a class ...