Related papers: On geometric aspects of diffuse groups

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution…

This is the first part of a series on non-compact groups acting isometrically on compact Lorentz manifolds. This subject was recently investigated by many authors. In the present part we investigate the dynamics of affine, and especially…

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…

In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…

We show that there is a smooth complex projective variety, of any dimension greater than or equal to two, whose automorphism group is discrete and not finitely generated. Moreover, this variety admits infinitely many real forms which are…

We lay the foundations for the study of relatively quasiconvex subgroups of relatively hyperbolic groups. These foundations require that we first work out a coherent theory of countable relatively hyperbolic groups (not necessarily finitely…

We take the fundamental group of the complement of the branch curve of a generic projection induced from canonical embedding of a surface. This group is stable on connected components of moduli spaces of surfaces. Since for many classes of…

We obtain sufficient conditions exlcuding the existence of non-trivial distribution sections of bundles over the boundary of symmetric spaces of negative curvature which are invariant with respect to a geometrically finite group of…

Recent progresses in single particle tracking have shown evidences of non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. A similar behavior has also been observed in…

We analyze loop-induced group-like symmetries in theories where fields are labeled by basis elements of a fusion algebra constructed from the conjugacy classes of finite groups. Although the fusion rules for conjugacy classes are in general…

This article initiates a geometric study of the automorphism groups of general graph products of groups, and investigates the algebraic and geometric structure of automorphism groups of cyclic product of groups. For a cyclic product of at…

We consider examples of the $\mathbb H$-type groups with the natural horizontal distribution generated by the commutation relations of the group. In the contrast with the previous studies we furnish the horizontal distribution with the…

We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups…

A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…

We consider 2-local geometries and other subgroup complexes for sporadic simple groups. For six groups, the fixed point set of a noncentral involution is shown to be equivariantly homotopy equivalent to a standard geometry for the component…

In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of symplectic groupoids give rise to discrete dynamical systems,…

We describe the endomorphisms of the direct product of two free groups of finite rank and obtain conditions for which the subgroup of fixed points is finitely generated and we do the same for periodic points. We also describe the…

We give conditions of an extension of a free group to be hyperbolic and relatively hyperbolic using the dynamics of the action of $\out$ on the complex of free factors combined with the weak attraction theory. We work with subgroups of…

We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…