Related papers: Small cancelation rings

We generalize first-species counterpoint theory to arbitrary rings and obtain some new counting and maximization results that enrich the theory of admitted successors, pointing to a structural approach, beyond computations. The…

We study the geometry of infinitely presented groups satisfying the small cancelation condition C'(1/8), and define a standard decomposition (called the criss-cross decomposition) for the elements of such groups. We use it to prove the…

We establish an Excision type theorem for niceness of group structure on the orbit space of unimodular rows of length $n$ modulo elementary action. This permits us to establish niceness for relative versions of results for the cases when $n…

A graph $\Gamma$ labelled by a set $S$ defines a group $G(\Gamma)$ whose generators are the set of labels $S$ and whose relations are all words which can be read on closed paths of this graph. We introduce the notion of aspherical graph and…

In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…

The machinery of framed (pre)sheaves was developed by Voevodsky [V1]. Based on the theory, framed motives of algebraic varieties are introduced and studied in [GP1]. An analog of Voevodsky's Cancellation Theorem [V1] is proved in this paper…

We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…

Let $G$ be the fundamental group of a three-manifold. By piecing together many known facts about three manifold groups, we establish two properties of the group ring $\mathbb{C}G$. We show that if $G$ has rational cohomological dimension…

We find new bounds on the conformal dimension of small cancellation groups. These are used to show that a random few relator group has conformal dimension 2+o(1) asymptotically almost surely (a.a.s.). In fact, if the number of relators…

We consider a series of groups defined by Kim and Manturov. These groups have their background in triangulations of a surface and configurations of points, lines or circles on the surface. They are expected to have relationships to many…

We show that the category of motivic spaces with transfers along finite flat morphisms, over a perfect field, satisfies all the properties we have come to expect of good categories of motives. In particular we establish the analog of…

This book is a rigorous and conceptually oriented introduction to ring theory. The emphasis is on structural understanding rather than encyclopedic coverage: rings are studied through ideals, homomorphisms, quotients, and universal…

Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…

In this note, we use the isomorphism of the ring of $G$-circulant matrices over a field $k$ with the group ring $k[G]$ to derive a very short proof of the Classical Maschke Theorem.

Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…

In Picard-Vessiot theory, the Galois theory for linear differential equations, the Picard-Vessiot ring plays an important role, since it is the Picard-Vessiot ring which is a torsor (principal homogeneous space) for the Galois group…

Let $X$ be a nonempty real variety that is invariant under the action of a reflection group $G$. We conjecture that if $X$ is defined in terms of the first $k$ basic invariants of $G$ (ordered by degree), then $X$ meets a $k$-dimensional…

We introduce partial group algebras with relations in a purely algebraic framework. Given a group and a set of relations, we define an algebraic partial action and prove that the resulting partial skew group ring is isomorphic to the…

We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem…

Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…