Related papers: A note on the structure of V(6) maps

The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.

The purpose of this note is to point to a gap in an argument in our paper "Stabilization for the automorphisms of free groups with boundaries", and explain how to fill it.

We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…

This note contains additions to the paper 'Clustered cell decomposition in P-minimal structures' (arXiv:1612.02683). We discuss a question which was raised in that paper, on the order of clustered cells. We also consider a notion of cells…

The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and…

The main purpose of this short note, on the one hand, to is rigorize some part of the proof of Theorem 1.3 in [11] in a simple way, and on the other hand, to give an alternative argument from local inequalities to global ones.

Part of these notes was written as the author's 2013 master thesis. For proper flat schemes over a complete discrete valuation ring of mixed characteristic, we construct an isomorphism of certain subgroups of the Picard group and the first…

In this note we give a precise statement and a detailed proof for reconstruction problem of weak bialgebra maps. As an application we characterize indecomposability of weak algebras in categorical setting.

The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.

This paper has been withdrawn by the author. The content of the previous versions is now covered by the more recent papers - math.DG/0610252 (concerning the Lie group structuren on the gauge groups) - math.DG/0612522 (concerning the weak…

The content of this preprint together with additional material appears now in 0706.2154.

The goal of this paper is to construct and describe certain arithmetic subgroups of the automorphism group of a partially commutative group. More precisely, given an arbitrary finite graph $\Gamma$ we construct an arithmetic subgroup…

We prove the analog of the Morel-Voevodsky localization theorem over complex analytic stacks, which is used in arXiv:2511.09371 to establish a 6-functor formalism of complex analytic motivic homotopy theory and produce an analytification…

The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.

The purpose of this note is to correct an inaccuracy in the paper: R.P. Agaev and P.Yu. Chebotarev, "On Determining the Eigenprojection and Components of a Matrix," Autom. Remote Control, 2002, vol. 63, pp. 1537-1545 [arXiv:math/0508197],…

The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.

We give a criterion for separability of subgroups of certain outer automorphism groups. This answers questions of Hagen and Sisto, by strengthening and generalizing a result of theirs on mapping class groups.

In earlier papers, we showed a decomposition of the arcs of 2-diregular digraphs (2-dds) and used it to prove some conditions for these graphs to be non-Hamiltonian; we then extended this decomposition to a larger class of digraphs and used…

The purpose of these notes is to give a categorical presentation/analysis of homotopy type theory. The notes are incomplete as they stand (October 2017). The chapter on univalent tribes is missing. The references are not always connected to…

This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…