The Bianchi groups are a family of discrete subgroups of PSL2(C) which have group theoretic descriptions as amalgamated products and HNN extensions. Using Bass-Serre theory, we show how the cohomology of these two constructions relates to the cohomology of their pieces. We then apply these results to calculate the mod-2 cohomology ring for various Bianchi groups.

A famous theorem of P. Novikov 1955 and W. W. Boone 1959 asserts the existence of a finitely presented group with unsolvable word problem. In my Spring 2005 topics course (MATH 574, Topics in Mathematical Logic), I presented Boone’s proof, as simplified by J. L. Britton, 1963. In this seminar I shall present a truly slick, streamlined proof, due to S. Aanderaa and D. E. Cohen, 1980. Instead of ...

This paper aims to solve a distributed resource allocation problem with binary local constraints. The is formulated as program cost function defined by the summation of agent costs plus global mismatch/penalty term. We propose modification Hopfield Neural Network (HNN) dynamics in order this while incorporating novel Newton-like weighting factor. addition lends itself fast avoidance saddle poin...

Abstract For more than three decades, the part of geoscientific community studying landslides through data-driven models has focused on estimating where may occur across a given landscape. This concept is widely known as landslide susceptibility. And, it seen vast improvement from old bivariate statistical techniques to modern deep learning routines. Despite all these advancements, no spatially...

Asymmetric HNN designed as an associative memory for query expansion has been researched in some papers. However, there is no criterion in this method to measure its validity and to tell good results from bad ones objectively. What’s more, convergence characteristic of HNNs may not be guaranteed if the symmetry is broken. Aiming at avoiding these two points, maximum mutual information (informax...

We discuss time complexity of The Conjugacy Problem in HNN-extensions of groups, in particular, in Miller’s groups. We show that for “almost all”, in some explicit sense, elements, the Conjugacy Problem is decidable in cubic time. It is worth noting that the Conjugacy Problem in a Miller group may have be undecidable. Our results show that “hard” instances of the problem comprise a negligibly s...

It is shown that the positive first-order theory of an HNN-extension G = 〈H, t; tat = φ(a)(a ∈ A)〉 can be reduced to the existential firstorder theory of G provided that A and B are proper subgroups of the base group H with A∩B finite. For an amalgamated free product G = H ∗A J , we show that the positive first-order theory of G can be reduced to the existential first-order theory of G in case ...