Related papers: Cubulating Small Cancellation Free Products
We define a notion of cofibration among n-categories and show that the cofibrant objects are exactly the free ones, that is those generated by polygraphs.
In this paper, we study the residual solvability of the generalized free product of solvable groups.
Factors $\frac{X}{Y}$ in a free group $F$ with $Y$ normal in $X$ are considered. Precise results on the free structure of ${Y}$ relative to the free structure of ${X}$ when $\frac{X}{Y}$ is abelian are obtained. Some extensions and…
For any $m \ge 1$ and odd prime power $\mathtt{q}=\mathtt{p}^m$, for $\mathtt{q}=2$, and for any $n \ge 1$, we show a result of decomposition for Pauli groups $\mathcal{P}_{n,\mathtt{q}}$ in terms of weak central products. This can be used…
In this paper, we study the geometry of cone-offs of CAT(0) cube complexes over a family of combinatorially convex subcomplexes, with an emphasis on their Gromov-hyperbolicity. A first application gives a direct cubical proof of the…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
We will obtain the warped product decompositions of spaces of constant curvature (with arbitrary signature) in their natural models as subsets of pseudo-Euclidean space. This generalizes the corresponding result by S. Nolker to arbitrary…
In this paper, we will construct the graph free product of noncommutative probability space. This is the attempt to explain and observe the combinatorial-object-depending probabilistic structure.
In this article we consider partial abelianization of associative algebra with respect to a subalgebra. This notion is a generalization of usual abelianization of associative algebra and has an application in Quantum Mechanics and Quantum…
Let $G/B$ be a flag variety over $\mathbb C$, where $G$ is a simple algebraic group with a simply laced Dynkin diagram, and $B$ is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity…
Symmetric product orbifolds, i.e. permutation orbifolds of the full symmetric group S_{n} are considered by applying the general techniques of permutation orbifolds. Generating functions for various quantities, e.g. the torus partition…
An approach to identify the normal subgroups determined by ideals in free group rings with the help of the derived functors of non-additive functors is explored. A similar approach, i.e., via derived functors, for computing limits of…
We study a family of finitely generated residually finite small cancellation groups. These groups are quotients of $F_2$ depending on a subset $S$ of positive integers. Varying $S$ yields continuously many groups up to quasi-isometry.
We describe an algorithm for deciding whether or not a given finitely generated torsion-free nilpotent group is decomposable as the direct product of nontrivial subgroups.
We study a class of quasimorphisms of the free group that can be expressed as infinite sums of Brooks quasimorphisms with some nice properties. We then review Heuer's framework of decompositions developed in arXiv:1710.03193, and put these…
We obtain a criterion for quasiconvexity of a subgroup of an amalgamated free product of two word hyperbolic groups along a virtually cyclic subgroup. The result provides a method of constructing new word hyperbolic group in class (Q), that…
Using dynamical techniques we show that there are no isolated elements on the space of left-preorders on a free product of two groups. As a consequence, when the groups are finitely generated, this space is either empty or a Cantor set. For…
This letter introduces a novel compact and lossless quantum microgrid formation (qMGF) approach to achieve efficient operational optimization of the power system and improvement of resilience. This is achieved through lossless reformulation…
Any virtually free group $H$ containing no non-trivial finite normal subgroup (e.g., the infinite dihedral group) is a retract of any finitely generated group containing $H$ as a verbally closed subgroup.
In this paper we study double cosets of finite rank free groups. We focus our attention on cancellation types in double cosets and their formal language properties.