Related papers: On some generalization of the M\"obius configurati…

Let $\overline{\mathcal{M}}_{g,n}$ be the moduli stack parametrizing Deligne-Mumford stable $n$-pointed genus $g$ curves and let $\overline{M}_{g,n}$ be its coarse moduli space: the Deligne-Mumford compactification of the moduli space of…

Suppose that $M$ is a connected orientable $n$-dimensional manifold and $m>2n$. If $H^i(M,\R)=0$ for $i>0$, it is proved that for each $m$ there is a monomorphism $H^m(W_n,\on{O}(n))\to H^m_{\on{cont}}(\on{Diff}M,\R)$. If $M$ is closed and…

A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given and…

We classify non symplectic prime order automorphisms and all finite order symplectic automorphism groups of generalised Kummer fourfolds using lattice theory and recent results on ample cones and monodromy groups. We study various geometric…

Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…

We denote by $\mathbb{M}^2_R$ a two dimensional space of constant positive Gaussian curvature. With methods of M\"obius geometry and using the classification of the M\"obius group of automorphisms ${\rm \bf Mob}_2 \, (\hat{\mathbb{C}})$ of…

Holomorphic quaternion functions only admit affine functions; thus, the M\"obius transformation for these functions, which we call quaternionic holomorphic transformation (QHT), only comprises similarity transformations. We determine a…

The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. Computing monodromy permutations using numerical algebraic geometry gives information about the…

A generalized Stiefel manifold is the manifold of orthonormal frames in a vector space with a non-degenerated bilinear or hermitian form. In this article, the Isometry group of the generalized Stiefel manifolds are computed at least up to…

We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…

We consider orthogonal representations $\eta_n:S_n \curvearrowright \mathbb{R}^N$ of the symmetry groups $S_n$, $n\ge 4$, with $N=n!/8$ motivated by symmetries of cross-ratios. For $n=5$ we find the decomposition of $\eta_5$ into…

We show that the (morphic) sequence $(-1)^{s_\varphi(n)}$ is asymptotically orthogonal to all bounded multiplicative functions, where $s_\varphi$ denotes the Zeckendorf sum-of-digits function. In particular we have $\sum_{n<N}…

Let $\phi$ be an automorphism of a free group $F_n$ of rank $n$, and let $M_{\phi}=F_n \rtimes_{\phi} \mathbb{Z}$ be the corresponding mapping torus of $\phi$. We study the group $Out(M_{\phi})$ under certain technical conditions on $\phi$.…

M\"obius transformations of the extended complex plane are at the crossroads of many interesting topics, e.g., they form a group under composition, are the simplest form of rational function, and are a path to Lie theory. Quaternionic…

Given a coassociative 4-fold N with a conical singularity in a varphi-closed 7-manifold M (a manifold endowed with a distinguished closed 3-form varphi), we construct a smooth family, {N'(t): t\in(0,tau)} for some tau>0, of (smooth,…

Let F be the field of two elements and G a finite abelian 2-group with an involutory automorphism. The extension of this automorphism to the group algebra FG is called an involutory involution. This determines the groups of unitary and…

We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For…

Let $\H^{n+1}$ denote the $n + 1$-dimensional (real) hyperbolic space. Let $\s^{n}$ denote the conformal boundary of the hyperbolic space. The group of conformal diffeomorphisms of $\s^n$ is denoted by $M (n)$. Let $M_o (n)$ be its identity…

We introduce a generalization of Weinstein's morphism, defined on \pi_{2k-1}(Ham(M,\omega)) for 1 < k \leq n, where (M,\omega) is a 2n-dimensional symplectic manifold. Using this morphism, we show that for n > 1 and 1 < k \leq n, the…

We give an explicit decomposition of $\hbox{Ind}(1)_{B_n}^{S_{2n}}$, following Barbasch and Vogan [1]. We define two natural generalizations of $B_n$, and extend the proof in [1] to recursively compute these decompositions. Although the…