Related papers: On the Berstein-Svarc Theorem in dimension 2

Let $P_k$ be the subgroup generated by $k$th powers of primitive elements in $F_r$, the free group of rank $r$. We show that $F_2/P_k$ is finite if and only if $k$ is $1$, $2$, or $3$. We also fully characterize $F_2/P_k$ for $k = 2,3,4$.…

Using standard results from higher (secondary) index theory, we prove that the positive scalar curvature bordism groups of a cartesian product GxZ are infinite in dimension 4n if n>0 G a group with non-trivial torsion. We construct…

Let V be the 7-dimensional irreducible representation of the quantum group U_q(g_2). For each n, there is a map from the braid group B_n to the endomorphism algebra of the n-th tensor power of V, given by R-matrices. We can extend this…

In this paper, we prove that the group $\mathrm{Aut}_\mathbb{Q}(X)$ of numerically trivial automorphisms are uniformly bounded for smooth projective threefolds $X$ of general type which either satisfy $q(X)\geq 3$ or have a Gorenstein…

Let $G$ be a group and $R$ be a ring. We define the Gorenstein homological dimension of $G$ over $R$, denoted by ${\rm Ghd}_{R}G$, as the Gorenstein flat dimension of trivial $RG$-module $R$. It is proved that ${\rm Ghd}_SG \leq {\rm…

Given a closed manifold M, we prove the upper bound of (n+d)/2 for the length of a product of systoles that can form a curvature-free lower bound for the total volume of M, in the spirit of M. Gromov's systolic inequalities. Here n is the…

For arbitrary level $N$, we relate the generating series of codimension 2 special cycles on $\mathcal{X}_{0}(N)$ to the derivatives of a genus 2 Eisenstein series, especially the singular terms of both sides. On the analytic side, we use…

Let $M$ be a simply connected closed $4$-manifold. It is proved that any (possibly finite) compact Lie group acting effectively and homologically trivially on $M$ by homeomorphisms is an abelian group of rank at most two. As applications,…

A theorem of Wiegerinck says that the Bergman space over any domain in $\mathbb C$ is either trivial or infinite dimensional. We generalize this theorem in the following form. Let E be a hermitian, holomorphic vector bundle over $\mathbb…

We prove that the group $\mathrm{SAut}_{\mathrm{k}}(\mathbb{A}^2)$ is simple as an algebraic group of infinite dimension, over any infinite field $\mathrm{k}$, by proving that any closed normal subgroup is either trivial or the whole group.…

The validity of Freedman's disk theorem is known to depend only on the fundamental group. It was conjectured that it fails for nonabelian free fundamental groups. If this were true then surgery theory would work in dimension four. Recently,…

Let p be a prime and F a field containing a primitive pth root of unity. Let E/F be a cyclic extension of degree p and G_E < G_F the associated absolute Galois groups. We determine precise conditions for the cohomology group…

Let $k$ be a field and let $\Omega$ be a universal domain over $k$. Let $f:X \r S$ be a dominant morphism defined over $k$ from a smooth projective variety $X$ to a smooth projective variety $S$ of dimension $\leq 2$ such that the general…

We compute the two-cocycles (or multipliers) of the free nilpotent groups of class $2$ and rank $n$ and give conditions for simplicity of the corresponding twisted group $C^*$-algebras. These groups are representation groups for…

CORRECTION. One of the main results in this paper contains a fatal error. We cannot conclude the existence of nontrivial vector bundles on X from the nontriviality of its K-group. The K-group that is computed here is the Grothendieck group…

It is shown that for any positive integer n there exists a subnormal weighted shift on a directed tree whose nth power is closed and densely defined while its (n + 1)th power has trivial domain. Similar result for composition operators in…

The main theorem is that if K is a finite CW complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X x S^n for any n greater than or equal to the…

We prove that the vector bundles at the core of the Knizhnik-Zamolodchikov and quantum constructions of braid groups representations are topologically trivial bundles. We provide partial generalizations of this result to generalized braid…

Let $K$ be a nontrivial knot. For each $n\in \mathbb{N}$, we prove that the rank of its $n$th iterated Whitehead doubled knot group $\pi_1(S^3 \setminus \operatorname{WD}^n(K))$ is bounded below by $n+1$. As an application, we show that…

We completely determine the free parts of the set-theoretic Yang-Baxter (co)homology groups of finite cyclic biquandles, along with fully computing the torsion subgroups of their 1st and 2nd homology groups. Furthermore, we provide upper…