We classify the “quotients” of a tannakian category in which the objects of a tannakian subcategory become trivial, and we examine the properties of such quotient categories.

Sufficient conditions are given for an elementary quotient of the kth Dilworth truncation of a matroid M to be the kth Dilworth truncation of a quotient of M. As special cases, contractions of Dilworth truncations and principal truncations by connected flats of Dilworth truncations are characterised as Dilworth truncations of certain matroids. As an application of the theory it is shown that th...

We prove estimates for the sectional curvature of hyperkähler quotients and give applications to moduli spaces of solutions to Nahm’s equations and Hitchin’s equations. This note was motivated by the following observation: the sectional curvature of the moduli space of charge k SU(2)-monopoles is bounded (by an explicit constant depending on normalisations). Unlike most statements about monopol...

In this paper we study quotients of Lie algebroids and groupoids endowed with compatible differential forms. We identify theoretic conditions under which such forms become basic characterize the induced on quotients. apply these results to describe generalized quotient reduction processes for (twisted) Poisson Dirac structures, as well their integration by (twisted, pre-)symplectic groupoids. p...

We introduce a new approach to the representation theory of reductive p-adic groups G, based on the Geometric Invariant Theory (GIT) of Moy-Prasad quotients. Stable functionals on these quotients are used to give a new construction of supercuspidal representations of G having small positive depth, called epipelagic. With some restrictions on p, we classify the stable and semistable functionals ...

We study some properties of A-homotopy groups: geometric interpretations of connectivity, excision results, and a re-interpretation of geometric quotients by solvable groups in terms of covering spaces in the sense of A-homotopy theory. These concepts and results are well-suited to the study of certain quotients via geometric invariant theory. As a case study in geometry of solvable group quoti...

Herrlich showed that a Mumford curve of genus g > 1 over the p-adic complex field Cp has at most 48(g− 1), 24(g− 1), 30(g− 1) or 12(g− 1) automorphisms as p = 2, 3, 5 or p > 5. The Mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p-adic triangle groups ∆p for p ≤ 5, or in a p-adic quadrangle group p for p > 5. The finite groups attaining these...

We use mirror formulas for the stable quotients analogue of Givental’s J-function for twisted projective invariants obtained in a previous paper to obtain mirror formulas for the analogues of the double and triple Givental’s J-functions (with descendants at all marked points) in this setting. We then observe that the genus 0 stable quotients invariants need not satisfy the divisor, string, or d...

Let G be a free-like group, meaning that G is either non-elementary (word) hyperbolic or G is large (in the sense of Gromov). In this paper we suggest several approaches to construct continuous families of periodic quotients of G which enjoy various properties. The first three methods work for any non-elementary hyperbolic group, producing three different continua of periodic quotients of G. Th...