Related papers: Toric arrangements and Bloch-Kato pro-$p$ groups

We study the Brauer groups of affine surfaces that are complements of singular hyperplane sections of smooth cubic surfaces over a field $k$ of characteristic $0$. We determine the Brauer group over the algebraic closure as a Galois module…

We show that there are contact 3-manifolds of support genus one which admit infinitely many Stein fillings, but do not admit arbitrarily large ones. These Stein fillings arise from genus-1 allowable Lefschetz fibrations with distinct…

We introduce and study a family of groups $\mathbf{BB}_n$, called the blocked-braid groups, which are quotients of Artin's braid groups $\mathbf{B}_n$, and have the corresponding symmetric groups $\Sigma_n$ as quotients. They are defined by…

For a complex Lie group G and a prime number p, Totaro had conjectured that the dimension of the singular cohomology with Z/p-coefficients of classifying space of G is bounded above by that of the de Rham cohomology of the classifying stack…

We define a new class of completions of locally symmetric varieties of type IV which interpolates between the Baily-Borel compactification and Mumford's toric compactifications. An arithmetic arrangement in a locally symmetric variety of…

Within the framework of braided or quasisymmetric monoidal categories braided Q-supersymmetry is investigated, where Q is a certain functorial isomorphism in a braided symmetric monoidal category. For an ordinary (co-)quasitriangular Hopf…

We examine the first non-vanishing higher homotopy group, $\pi_p$, of the complement of a hypersolvable, non--supersolvable, complex hyperplane arrangement, as a module over the group ring of the fundamental group, $\Z\pi_1$. We give a…

We study the finiteness properties of the braided Higman--Thompson group $bV_{d,r}(H)$ with labels in $H\leq B_d$, and $bF_{d,r}(H)$ and $bT_{d,r}(H)$ with labels in $H\leq PB_d$ where $B_d$ is the braid group with $d$ strings and $PB_d$ is…

Slattery has generalized Brauer's theory of p-blocks of finite groups to pi-blocks of pi-separable groups where pi is a set of primes. In this setting we show that the order of a defect group of a pi-block B is bounded in terms of the…

We completely describe the finitely generated pro-$p$ subgroups of the profinite completion of the fundamental group of an arbitrary $3$-manifold. We also prove a pro-$p$ analogue of the main theorem of Bass--Serre theory for finitely…

It was well known that there are $e$-particles and $m$-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional $\mathbb{Z}_2$ topological order. Recent mathematical result, however, shows that…

We give an algorithm that takes a smooth hypersurface over a number field and computes a $p$-adic approximation of the obstruction map on the Tate classes of a finite reduction. This gives an upper bound on the "middle Picard number" of the…

We produce an explicit description of the K-theory and K-homology of the pure braid group on $n$ strands. We describe the Baum--Connes correspondence between the generators of the left- and right-hand sides for $n=4$. Using functoriality of…

We extend work of Davis and Januszkiewicz by considering {\it omnioriented} toric manifolds, whose canonical codimension-2 submanifolds are independently oriented. We show that each omniorientation induces a canonical stably complex…

The nonorientable four-ball genus of a knot $K$ in $S^3$ is the minimal first Betti number of nonorientable surfaces in $B^4$ bounded by $K$. By amalgamating ideas from involutive knot Floer homology and unoriented knot Floer homology, we…

Computation of the fundamental group of the complement in the complex plane of the branch curve S , of a generic projection of the Veronese surface to the plane is presented. This paper is a continuation of our previous papers: Braid Group…

This paper will appear in the Santa Cruz proceedings. An overview of the braid group techniques in the theory of algebraic surfaces, from Zariski to the latest results, is presented. An outline of the Van Kampen algorithm for computing…

We consider a simple modification of the Chow group CH^2(Spec(k),3) using only linear subvarieties in affine spaces and show that it maps surjectively to the Bloch group B(k) for any infinite field k. We also describe the kernel of this…

In the paper, we study special configurations of lines and points in the complex projective plane, so called k-nets. We describe the role of these configurations in studies of cohomology on arrangement complements. Our most general result…

We define a monoid structure on the set of $k$-equal arrangements and use this structure to define limits of braid arrangements. We compute the cohomology of the associated limits of rational models of the arrangements complex complements.…