Related papers: On a question of Brendle and Benson

We provide a short proof that the dimensions of the mod $p$ homology groups of the unordered configuration space $B_k(T)$ of $k$ points in a torus are the same as its Betti numbers for $p>2$ and $k\leq p$. Hence the integral homology has no…

In this paper, we prove that each automorphism of the Torelli group of a surface is induced by a diffeomorphism of the surface, provided that the surface is a closed, connected, orientable surface of genus at least 3. This result was…

This work is NOT to be used as reference. First, because as C.F.~B\"odigheimer and M.~Korkmaz pointed to us the computation of the $\mathbf{Z}_2$ factor that remained undecided in M.~Korkmaz and A. Stipsicz, {\em The second homology groups…

Thomassen proved that every planar graph $G$ on $n$ vertices has at least $2^{n/9}$ distinct $L$-colorings if $L$ is a 5-list-assignment for $G$ and at least $2^{n/10000}$ distinct $L$-colorings if $L$ is a 3-list-assignment for $G$ and $G$…

We prove that the mapping class group of a closed oriented surface of genus at least two does not have Kazhdan's property (T).

Babai and S\'os have asked whether there exists a constant c>0 such that every finite group G has a product-free subset of size at least c|G|: that is, a subset X that does not contain three elements x, y and z with xy=z. In this paper we…

We construct two different families of properly Alexandrov-immersed surfaces in $\mathbb{H}^2\times \mathbb{R}$ with constant mean curvature $0<H\leq \frac 1 2$, genus one and $k\geq2$ ends ($k=2$ only for one of these families). These ends…

Let $S$ be a surface of nonpositive curvature of genus bigger than 1 (i.e. not the torus). We prove that any flat strip in the surface is in fact a flat cylinder. Moreover we prove that the number of homotopy classes of such flat cylinders…

Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with…

Let $K$ and $k$ be $p$-adic fields. Let $L$ be the composite field of $K$ and a certain Lubin-Tate extension over $k$ (including the case where $L=K(\mu_{p^{\infty}})$). In this paper, we show that there exists an explicitly described…

We show that every subgroup of the mapping class group MCG(S) of a compact surface S is either virtually abelian or it has infinite dimensional second bounded cohomology. As an application, we give another proof of the…

Frieze patterns of integers were studied by Conway and Coxeter. Let $\mathscr{C}$ be the cluster category of Dynkin type $A_n$. Indecomposables in $\mathscr{C}$ correspond to diagonals in an $(n+3)$-gon. Work done by Caldero and Chapoton…

Over a one-dimensional Gorenstein local domain $R$, let $E$ be the endomorphism ring of the maximal of $R$, viewed as a subring of the integral closure $\overline R$. If there exist finitely generated $R$-modules $M$ and $N$, neither of…

We prove that the mapping class group of the one-holed Cantor tree surface is acyclic. This in turn determines the homology of the mapping class group of the once-punctured Cantor tree surface (i.e. the plane minus a Cantor set), in…

We show that on a nonorientable surface of genus at least 7 any power of a Dehn twist is equal to a single commutator in the mapping class group and the same is true, under additional assumptions, for the twist subgroup, and also for the…

Let $M$ be a smooth connected orientable compact surface. Denote by $F(M,S^1)$ the space of all Morse functions $f:M\to S^1$ having no critical points on the boundary of $M$ and such that for every boundary component $V$ of $M$ the…

Let $(X,\omega)$ be a compact symplectic manifold of dimension $2n$ and let $Ham(X,\omega)$ be its group of Hamiltonian diffeomorphisms. We prove the existence of a constant $C$, depending on $X$ but not on $\omega$, such that any finite…

Suppose $C$ is a smooth projective curve of genus 1 over a perfect field $F$, and $E$ is its Jacobian. In the case that $C$ has no $F$-rational points, so that $C$ and $E$ are not isomorphic, $C$ is an $E$-torsor with a class $\delta(C)\in…

We prove that a uniform pro-p group with no nonabelian free subgroups has a normal series with torsion-free abelian factors. We discuss this in relation to unique product groups. We also consider generalizations of Hantzsche-Wendt groups.

The mapping class group ${\Gamma}_g^ 1$ of a closed orientable surface of genus $g \geq 1$ with one marked point can be identified, by the Nielsen action, with a subgroup of the group of orientation preserving homeomorphims of the circle.…