Related papers: SAut(Fn) cannot act on small tori

In this paper, the well-known relationship between theta functions and Heisenberg group actions thereon is resumed by combining complex algebraic and noncommutative geometric techniques in that we describe Hermitian-Einstein vector bundles…

We show that the automorphism group of a one-dimensional full shift (the group of reversible cellular automata) does not satisfy the Tits alternative. That is, we construct a finitely-generated subgroup which is not virtually solvable yet…

Working over a field $k$ of characteristic zero, we study the ring $\mathfrak{R}=\mathfrak{D}^{\mathbb{Z}_2}$ where $\mathfrak{D}=k[x_0,x_1,x_2]/(2x_0x_2-x_1^2-1)$ and $\mathbb{Z}_2$ acts by $x_i\to -x_i$. $\mathfrak{D}$ admits an algebraic…

We study the relation between class S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two dimensional torus with punctures. Turning on the self dual $\Omega$-background corresponds to a…

The famous theorem of Matsumura-Oort states that if $X$ is a proper scheme, then the automorphism group functor $\mathfrak{Aut}(X)$ of $X$ is a locally algebraic group scheme. In this paper we generalize this theorem to the category of…

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra. Moreover, any II$_1$ factor of the form $Q \vt L(\Bbb F_r) $, with $Q$ an arbitrary subfactor…

We consider genus one n-point functions for a vertex operator superalgebra with a real grading. We compute all n-point functions for rank one and rank two fermion vertex operator superalgebras. In the rank two fermion case, we obtain all…

We prove that if a finite group $G$ acts smoothly on a manifold $M$ so that all the isotropy subgroups are abelian groups with rank $\leq k$, then $G$ acts freely and smoothly on $M \times \bbS^{n_1} \times...\times \bbS^{n_k}$ for some…

In this paper, we show local smooth rigidity for higher rank ergodic nilpotent action by toral automorphisms and prove the existence of such action on any torus TN for any even N ? 6. We also give examples of smooth rigidity of actions…

The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…

In this paper we study smooth orientation-preserving free actions of the cyclic group $\mathbb Z/m$ on a class of $(n-1)$-connected $2n$-manifolds, $\sharp g (S^n \times S^n)\sharp \Sigma$, where $\Sigma$ is a homotopy $2n$-sphere. When…

Let $G$ be a group acting freely, properly discontinuously and cellularly on a finite dimensional $C$W-complex $\Sigma(2n)$ which has the homotopy type of the $2n$- sphere $\mathbb{S}^{2n}$. Then, this action induces an action of the group…

We describe a simple criterion for showing that a group has Serre's property FA. By exhibiting a certain pattern of finite subgroups, we show that this criterion is satisfied by Aut(F_n) and SL(n,Z) when n>=3.

In this paper, we study isometric actions on finite-dimensional CAT(0) spaces for the Higman-Thompson groups $T_n$, which are generalizations of Thompson's group $T$. It is known that every semi-simple action of $T$ on a complete CAT(0)…

For an amalgam of two free groups and a particular kind of automorphism, we show that the Dehn function of the corresponding mapping torus is quadratic.

We study the representations of the group $\mathbb{Z}_2^{*n}$, the free product of $\mathbb{Z}_2$ with itself $n$-times. We use the action of $B_n = S_2 \wr S_n $ as algebra automorphisms on the group algebra $\mathbb{C}(\mathbb{Z}_2^{*n})$…

We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a…

This paper develops further the theory of the automorphic group of non-constant entire functions. This theory has already a long history that essentially started with two remarkable papers of Tatsujir\^o Shimizu that were published in 1931.…

We show that the automorphism group of affine n-space $A^n$ determines $A^n$ up to isomorphism: If $X$ is a connected affine variety such that $Aut(X)$ is isomorphic to $Aut(A^n)$ as ind-groups, then $X$ is isomorphic to $A^n$ as a variety.…

On a smooth closed oriented $4$-manifold $M$ with a smooth action by a compact Lie group $G$, we define a $G$-monopole class as an element of $H^2(M;\Bbb Z)$ which is the first Chern class of a $G$-equivariant Spin$^c$ structure which has a…