The study of stable isotopy classes a finite collection immersed circles without triple or higher intersections on closed oriented surfaces is considered as planar analogue virtual knot theory, far reaching generalisation classical theory. Recent works have established Alexander and Markov theorems in the setting. In case, role groups played by twin groups, class right-angled Coxeter groups. A ...

We develop a Harder-Narasimhan theory for Kisin modules generalizing a similar theory for finite flat group schemes due to Fargues [Far10]. We prove the tensor product theorem, i.e., that the tensor product of semistable objects is again semi-stable. We then apply the tensor product theorem to the study of Kisin varieties for arbitrary connected reductive groups.

This paper considers coorbit spaces parametrized by mixed, weighted Lebesgue with respect to the quasi-regular representation of semi-direct product Euclidean space and a suitable matrix dilation group. The class groups that we allow, so-called integrably admissible groups, contains yielding an irreducible, square-integrable as proper subclass. obtained scale extends therefore well-studied wave...