The presence of magnetic monopole like excitations of nonabelian varieties is one of the subtlest consequences of spontaneously broken gauge symmetries. Important hints about their quantum mechanical properties, which remained long mysterious, are coming from a detailed knowledge of the dynamics of supersymmetric gauge theories which has become available recently. These developments might shed ...

We investigate the wormhole solutions that arise in the semiclassical analysis of euclidean gravity coupled to gauge fields. In 2 + 1 dimensions, "magnetic monopole" solutions can be constructed, for either abelian or nonabelian gauge fields. The low-energy physics induced by these wormholes qualitatively resembles, but is quantitatively distinguishable from, the tow-energy physics of a gauge t...

The notion of an amenable equivalence relation was introduced by Zimmer in the course of his analysis of orbit equivalence relations in ergodic theory (see [12]). Recently it played an important role in Monod’s striking family of examples of nonamenable groups which do not contain nonabelian free subgroups. If A is a subring of R, define H(A) to be the group of all piecewise PSL2(A) homeomorphi...

A nonabelian finite flavor group G ⊂ SO(3) can have double covering G ′ ⊂ SU(2) such that G 6⊂ G ′ . This situation is not contradictory, but quite natural, and we give explicit examples such as G = Dn, G ′ = Q2n and G = T,G ′ = T ′ . This observation can be crucial in particle theory model building. [email protected] [email protected] [email protected]

A construction is given of a valent arc transitive graph with vertex stabilizer isomorphic to the dihedral group D The graph has vertices and is the rst known example of a valent arc transitive graph with nonabelian vertex stabilizer A VALENT HALF ARC TRANSITIVE GRAPH

In this work we consider a generalization of graph flows. A flow is, in its simplest formulation, labelling the directed edges with real numbers subject to various constraints. common constraint is conservation vertex, meaning that sum labels on incoming vertex equals those outgoing edges. One easy fact if conserving all but one then it also remaining one. our do not label numbers, elements fro...

We look at Hopf Galois structures with square free pqw degree on separable field extensions (nonnormal) L/K. Where E/K is the normal closure of L/K, group permutation G = Gal(E/K). study details nonabelian case, where Jl ⟨σ, [τ, αl ]⟩ a regular subgroup Hol(N) for 1 ≤ l w − 1. first find G, and then each G. In this there exists four such that are admissible within

It was previously shown by Grunewald and Lubotzky that the automorphism group of a free group, $\operatorname{Aut}(F\_n)$, has large collection virtual arithmetic quotients. Analogous results were proved for mapping class Looijenga Grunewald, Larsen, Lubotzky, Malestein. In this paper, we prove analogous right-angled Artin defining graphs. As corollary our methods produce new quotients $\operat...