We study two–generated subgroups x f , gy Homeo pIq such that x f 2, g2y is isomorphic to Thompson’s group F, and such that the supports of f and g form a chain of two intervals. We show that this class contains uncountably many isomorphism types. These include examples with nonabelian free subgroups, examples which do not admit faithful actions by C2 diffeomorphisms on 1–manifolds, examples ...

An iterative Noether scheme, advocated by Deser, is used to introduce gauge invariant couplings nonrelativistic matter with global symmetries related usual charge conservation and dipole recently discussed in fractonic theories. No reference any principle, or otherwise, required. A dual description found where the theory defined either terms of vector field or, alternatively, higher derivatives...

The prime graph of a finite group $G$ is denoted by$ga(G)$. A nonabelian simple group $G$ is called quasirecognizable by primegraph, if for every finite group $H$, where $ga(H)=ga(G)$, thereexists a nonabelian composition factor of $H$ which is isomorphic to$G$. Until now, it is proved that some finite linear simple groups arequasirecognizable by prime graph, for instance, the linear groups $L_...

We propose a definition of “nonabelian mixed Hodge structure” together with a construction associating to a smooth projective variety X and to a nonabelian mixed Hodge structure V , the “nonabelian cohomology of X with coefficients in V ” which is a (pre-)nonabelian mixed Hodge structure denoted H = Hom(XM , V ). We describe the basic definitions and then give some conjectures saying what is su...

A remarkable feature of D-branes is the appearance of a nonabelian gauge theory in the description of several (nearly) coincident branes. This nonabelian structure plays an important role in realizing various geometric effects with D-branes. In particular, the branes’ transverse displacements are described by matrix-valued scalar fields and so noncommutative geometry naturally appears in this f...

The properties of BPS monopoles carrying nonabelian magnetic charges are investigated by following the behavior of the moduli space of solutions as the Higgs field is varied from a value giving a purely abelian symmetry breaking to one that leaves a nonabelian subgroup of the gauge symmetry unbroken. As the limit of nonabelian unbroken symmetry is reached, some of the fundamental abelian monopo...

Whereas usual Hodge theory concerns mainly the usual or abelian cohomology of an algebraic variety—or eventually the rational homotopy theory or nilpotent completion of π1 which are in some sense obtained by extensions—nonabelian Hodge theory concerns the cohomology of a variety with nonabelian coefficients. Because of the basic fact that homotopy groups in higher dimensions are abelian, and si...