We prove some conditions for higher-dimensional algebraic fibering of pro-p group extensions, and we establish corollaries about incoherence of pro-p groups. In particular, if is a short exact sequence of pro-p groups, such that contains a finitely g…
Building on work of Furstenberg and Tzkoni, we introduce -flag affine quermassintegrals and their dual versions. These quantities generalize affine and dual affine quermassintegrals as averages on flag manifolds (where the Grassmannian can be considere…
We study monotone operators in reflexive Banach spaces that are invariant with respect to a group of suitable isometric isomorphisms, and we show that they always admit a maximal extension which preserves the same invariance. A similar result applies t…
Let be integers. Denote by the set of complex matrices and the norm on with a positive integer and a real number . We show that a linear map satisfies if and only if there exist unitary matrices such that where is the identity map or the tran…
In this paper, we study the Dirichlet problem of Hessian quotient equations of the form in exterior domains. For , we obtain the necessary and sufficient conditions on the existence of radially symmetric solutions. For g being a perturbation of a gene…
The Hoffman ratio bound, Lovász theta function, and Schrijver theta function are classical upper bounds for the independence number of graphs, which are useful in graph theory, extremal combinatorics, and information theory. By using generalized invers…
Let G be a compact quantum group. We show that given a G-equivariant -correspondence E, the Pimsner algebra can be naturally made into a G–algebra. We also provide sufficient conditions under which it is guaranteed that a G-action on the Pimsner alge…
We provide a purely combinatorial proof of a skein exact sequence obeyed by double-point enhanced grid homology. We also extend the theory to coefficients over and discuss alternatives to the Ozsváth–Szabó invariant.
Let G be a complex classical group, and let V be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of G-invariant polynomial funct…
An old question of Arhangel’skii asks if the Menger property of a Tychonoff space X is preserved by homeomorphisms of the space of continuous real-valued functions on X endowed with the pointwise topology. We provide affirmative answer in the case of …