JSJ-decompositions of finitely presented groups and complexes of groups

A JSJ-splitting of a group $G$ over a certain class of subgroups is a graph of groups decomposition of $G$ which describes all possible decompositions of $G$ as an amalgamated product or an HNN extension over subgroups lying in the given class. Such decompositions originated in 3-manifold topology. In this paper we generalize the JSJ-splitting constructions of Sela, Rips-Sela and Dunwoody-Sageev and we construct a JSJ-splitting for any finitely presented group with respect to the class of all slender subgroups along which the group splits. Our approach relies on Haefliger's theory of group actions on CAT$(0)$ spaces

Simple Amplitudes for \Phi^3 Feynman Ladder Graphs

Recently, we proposed a new approach for calculating Feynman graphs amplitude using the Gaussian representation for propagators which was proven to be exact in the limit of graphs having an infinite number of loops. Regge behavior was also found in a completely new way and the leading Regge trajectory calculated. Here we present symmetry arguments justifying the simple form used for the polynomials in the Feynman parameters $\bar \alpha _{\ell}$, where $\bar \alpha _{\ell}$ is the mean-value for these parameters, appearing in the amplitude for the ladder graphs. (Taking mean-values is equivalent to the Gaussian representation for propagators).Comment: 11 Plain TeX pages, 2 PostScript figures include

The Unified Segment Tree and its Application to the Rectangle Intersection Problem

In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that arise naturally in this variation, and we show some properties concerning the relationships between the nodes, and the regions those nodes represent. We think these properties will enable the data to be utilized in new situations, beyond those previously studied. As an example, we show that the data structure can be used to solve the Rectangle Intersection Problem in a more straightforward and natural way than had be done in the past.Comment: 14 pages, 6 figure

On a Subposet of the Tamari Lattice

We explore some of the properties of a subposet of the Tamari lattice introduced by Pallo, which we call the comb poset. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees. We relate this poset to a partial order on the symmetric group studied by Edelman.Comment: 21 page

Sussing merger trees: a proposed merger tree data format

We propose a common terminology for use in describing both temporal merger trees and spatial structure trees for dark-matter halos. We specify a unified data format in HDF5 and provide example I/O routines in C, FORTRAN and PYTHON