Let X be a polyhedral complex with finitely many isometry classes of links. We establish a restriction on the covolumes of uniform lattices acting on X. When X is two-dimensional and has all links isometric to either a complete bipartite graph or the building for a Chevalley group of rank 2 over a field of prime order, we obtain further restrictions on covolumes.

We prove that if G is a non-uniform lattice in a rank-one semisimple Lie group = Isom(H2 R ), then G is quasi-isometrically co-Hopf. This means that every quasi-isometric embedding G → G is coarsely surjective and thus is a quasi-isometry.

The linear code equivalence problem is to decide whether two linear codes over Fq are identical up to a linear isometry of the Hamming space. The support splitting algorithm [25] runs in polynomial time for all but a negligible proportion of all linear codes, and solves the latter problem by recovering the isometry when it is just a permutation of the code support. While for a binary alphabet i...

Geometric group theory is the study of the relationship between the algebraic, geometric, and combinatorial properties of finitely generated groups. Here, we add to the dictionary of correspondences between geometric group theory and computational complexity. We then use these correspondences to establish limitations on certain models of computation. In particular, we establish a connection bet...

Suppose G is a hyperbolic group whose boundary ∂∞G has topological dimension k. If ∂∞G is quasi-symmetrically homeomorphic to an Ahlfors kregular metric space, then, modulo a finite normal subgroup, G is isomorphic to a uniform lattice in the isometry group Isom(Hk+1) of hyperbolic (k+1)-space.

We calculate the scalar potential in the gauged N=2 supergravity with a single hypermultiplet, whose generic quaternionic moduli space metric has an abelian isometry. This isometry is gauged by the use of a graviphoton gauge field. The hypermultiplet metric and the scalar potential are both governed by the single real potential that is a solution to the 3d (integrable) continuous Toda equation....

Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this property with optimal parameters are mainly obtained via probabilistic arguments. Given any matrix, deciding whether it satisfies the restricted isometry property i...

Given polar spaces (V, β) and (V, Q) where V is a vector space over a field K, β a reflexive sesquilinear form and Q a quadratic form, we have associated classical isometry groups. Given a subfield F of K and an F -linear function L : K → F we can define new spaces (V, Lβ) and (V, LQ) which are polar spaces over F . The construction so described gives an embedding of the isometry groups of (V, ...

Abstract We prove that every bijection preserving triple transition pseudo-probabilities between the sets of minimal tripotents two atomic JBW $$^*$$ ∗ -triples automatically preserves orthogonality in both directions. Consequently, each is precisely restriction a (complex-...

The main aim of the classification of linear codes is the evaluation of complete lists of representatives of the isometry classes. These classes are mostly defined with respect to linear isometry, but it is well known that there is also the more general definition of semilinear isometry taking the field automorphisms into account. This notion leads to bigger classes so the data becomes smaller....