Related papers: (Un)distorted stabilisers in the handlebody group
We stabilize nematic droplets with handles against surface-tension-driven instabilities using a yield-stress material as outer fluid and study the complex nematic textures and defect structures that result from the competition between…
In a previous paper we have introduced the notion of geometric directional bundle of a singular space, in order to introduce global bi-Lipschitz invariants. Then we have posed the question of whether or not the geometric directional bundle…
We study the stability of pencils of plane sextics in the sense of geometric invariant theory. In particular, we obtain a complete and geometric description of the stability of Halphen pencils of index two.
A discrete group is matricially stable if every function from the group to a complex unitary group that is "almost multiplicative" in the point-operator norm topology is "close" to a genuine unitary representation. It follows from a recent…
A class of groups is investigated, each of which has a fairly simple presentation . For example the group $R = (a, b, c, d | a^3 = b^3 = c^3 = d^3 = 1, ba^{-1} =dc^{-1}, ca^{-1} = db^{-1}) $ is in the class. Such a group does not have as a…
We discuss the role of tangential stabilization in a curvature driven flow of planar curves. The governing system of nonlinear parabolic equations includes a nontrivial tangential velocity functional yielding a uniform redistribution of…
We prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2…
We prove twisted homological stability with polynomial coefficients for automorphism groups of free nilpotent groups of any given class. These groups interpolate between two extremes for which homological stability was known before, the…
We provide a new approach to stable ergodicity of systems with dominated splittings, based on a geometrical analysis of global stable and unstable manifolds of hyperbolic points. Our method suggests that the lack of uniform size of Pesin's…
A new type of stellarator divertor is found. It has features of both a nonresonant divertor (A. Punjabi and A. H. Boozer, Phys. Plasmas 27, 012503 (2020)) as well as a resonant divertor. It has the outermost confining surface with sharp…
Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An…
In this note we discuss dynamical mechanisms for brane stabilization in the brane world context. In particular, we consider supersymmetry preserving brane stabilization, and also brane stabilization accompanied by supersymmetry breaking.…
We study the automorphisms of binary stabilizer codes and states. We prove that they almost always form a solvable group, and thereby shed new light on the fact that there is no universal set of transversal gates. We also determine the…
Using the Galatius--Kupers--Randal-Williams framework of cellular $E_2$-algebras, we prove a secondary stability theorem for mapping class groups of nonorientable surfaces. As a corollary, we obtain a new best known stability range for the…
We compute the \'etale cohomology groups H^i(X,G_m) in several cases, where X is a smooth tame Deligne-Mumford stack of dimension 1 over an algebraically closed field. We have complete results for orbicurves (and, more generally, for…
In this paper we prove stability results for the homology of the mapping class group of a surface. We get a stability range that is near optimal, and extend the result to twisted coefficients.
Let $G$ be a permutation group on the finite set $\Omega$. We prove various results about partitions of $\Omega$ whose stabilizers have good properties. In particular, in every solvable permutation group there is a set-stabilizer whose…
The homology groups of the automorphism group of a free group are known to stabilize as the number of generators of the free group goes to infinity, and this paper relativizes this result to a family of groups that can be defined in terms…
The object of this paper is the notion of r-spin structure: a line bundle whose r-th power is isomorphic to the canonical bundle. Over the moduli functor M_g of smooth genus-$g$ curves, $r$-spin structures form a finite torsor under the…
Topological point defects on orientationally ordered spheres, and on deformable fluid vesicles have been partly motivated by their potential applications in creating super-atoms with directional bonds through functionalization of the…