38 research outputs found
Aspherical Word Labeled Oriented Graphs and Cyclically Presented Groups
A {\em word labeled oriented graph} (WLOG) is an oriented graph on
vertices , where each oriented edge is labeled by a
word in . WLOGs give rise to presentations which generalize Wirtinger
presentations of knots. WLOG presentations, where the underlying graph is a
tree are of central importance in view of Whitehead's Asphericity Conjecture.
We present a class of aspherical world labeled oriented graphs. This class can
be used to produce highly non-injective aspherical labeled oriented trees and
also aspherical cyclically presented groups.Comment: 7 pages, 3 figure
Ribbon 2-knot groups of Coxeter type
Wirtinger presentations of deficiency 1 appear in the context of knots, long
virtual knots, and ribbon 2-knots. They are encoded by (word) labeled oriented
trees and, for that reason, are also called LOT presentations. These
presentations are a well known and important testing ground for the validity
(or failure) of Whitehead's asphericity conjecture. In this paper we define
LOTs of Coxeter type and show that for every given there exists a (prime)
LOT of Coxeter type with group of rank . We also show that label separated
Coxeter LOTs are aspherical
On the \u3ci\u3eK\u3c/i\u3e-Theory and Homotopy Theory of the Klein Bottle Group
We construct infinitely many chain homotopically distinct algebraic 2-complexes for the Klein bottle group and give various topological applications. We compare our examples to other examples in the literature and address the question of geometric realizability
The Local Structure of Injective LOT-Complexes
Labeled oriented trees, LOT's, encode spines of ribbon discs in the 4-ball
and ribbon 2-knots in the 4-sphere. The unresolved asphericity question for
these spines is a major test case for Whitehead's asphericity conjecture. In
this paper we give a complete description of the link of a reduced injective
LOT complex. An important case is the following: If is a reduced
injective LOT that does not contain boundary reduced sub-LOTs, then
is a bi-forest. As a consequence is aspherical, in
fact DR, and its fundamental group is locally indicable. We also show that a
general injective LOT complex is aspherical. Some of our results have already
appeared in print over the last two decades and are collected here
The Σ2-conjecture for metabelian groups: the general case
AbstractThe Bieri–Neumann–Strebel invariant Σm(G) of a group G is a certain subset of a sphere that contains information about finiteness properties of subgroups of G. In case of a metabelian group G the set Σ1(G) completely characterizes finite presentability and it is conjectured that it also contains complete information about the higher finiteness properties (FPm-conjecture). The Σm-conjecture states how the higher invariants are obtained from Σ1(G). In this paper we prove the Σ2-conjecture
Gluon-Induced Weak Boson Fusion
The gluon-gluon induced terms for Higgs production through weak boson fusion
(WBF) are computed. Formally, these are of NNLO in the strong coupling
constant. This is the lowest order at which non-zero color exchange occurs
between the scattering quarks, leading to a color field and thus additional
hadronic activity between the outgoing jets. Using a minimal set of cuts, the
numerical impact of these terms is at the percent level with respect to the NLO
rate for weak boson fusion. Applying the so-called WBF cuts leads to an even
stronger suppression, so that we do not expect a significant deterioration of
the WFB signal by these color exchange effects.Comment: 9 pages, 8 figures (21 included ps- and eps-files