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This work investigates the rank properties of $A^+(B_n)$, the multiplicative semigroup reduct of the affine near-semirings over an aperiodic Brandt semigroup $B_n$. In this connection, the work obtains the small rank, lower rank and large…

We study virtual retracts in groups acting on rooted trees. We show that finitely generated branch groups do not have the local retraction (LR) property. Furthermore, we specialize to iterated monodromy groups of post-critically finite…

A link in the 3-sphere is homotopically trivial, according to Milnor, if its components bound disjoint maps of disks in the 4-ball. This paper concerns the question of what spaces give rise to the same class of homotopically trivial links…

It is an old and challenging topic to investigate for which discrete groups G the full group C*-algebra C*(G) is residually finite-dimensional (RFD). In particular not much is known about how the RFD property behaves under fundamental…

A braided fusion category is said to have Property $\textbf{F}$ if the associated braid group representations factor over a finite group. We verify integral metaplectic modular categories have property $\textbf{F}$ by showing these…

We generalize presentations of the fundamental group of discriminant complements and arrive at a class of presentations associated naturally with words in the free monoid of the alphabet $\sigma_1,\dots,\sigma_{n-1}$. Our study addresses…

Main Theorem (3.3): Let $M$ be a compact four-dimensional manifold either with curvature, positive on complex isotropic two-planes, or self-dual of positive scalar curvature. If $\pi_1 (M)$ admits a nontrivial unitary representation, and…

By the results of the author and Chiantini in Math.AG/0110102, on a general quintic threefold $X \subset {\mathbf P}^4$ the minimum integer $p$ for which there exists a positive dimensional family of irreducible rank $p$ vector bundles on…

Following previous work on congruence subgroups and crystallographic braid groups, we study the lower central series of congruence braid groups related to the braid group $B_3$, showing in particular that corresponding quotients are almost…

In this article, we study the space of subgroups of non-amenable generalized Baumslag-Solitar groups (GBS groups) of rank $d$, that is, groups acting cocompactly on an oriented tree with vertex and edge stabilizers isomorphic to…

In this article we prove that the arithmetic profinite iterated monodromy group of a post-critically infinite unicritical polynomial is regular branch (and so of positive Hausdorff dimension), and has positive fixed-point proportion when…

In [2], an exhaustive construction is achieved for the class of all 4-dimensional unital division algebras over finite fields of odd order, whose left nucleus is not minimal and whose automorphism group contains Klein's four-group. We…

Given a closed smooth manifold $M$ of even dimension $2n\ge6$ with finite fundamental group, we show that the classifying space ${\rm BDiff}(M)$ of the diffeomorphism group of $M$ is of finite type and has finitely generated homotopy groups…

Let n\geq 3. We classify the finite groups which are realised as subgroups of the sphere braid group B_n(S^2). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal…

We prove that the coinvariant ring of the irreducible Coxeter group of type H4 has the strong Lefschetz property.

Let $f_t(z)=z^2+t$. For any $z\in\mathbb{Q}$, let $S_z$ be the collection of $t\in\mathbb{Q}$ such that $z$ is preperiodic for $f_t$. In this article, assuming a well-known conjecture of Flynn, Poonen, and Schaefer, we prove a uniform…

We construct a torsion-free arithmetic lattice in $\mathrm{PGL}_2(\mathbb{F}_2(\!(t)\!))\times\mathrm{PGL}_2(\mathbb{F}_2(\!(t)\!))$ arising from a quaternion algebra over $\mathbb{F}_2(z)$. It is the fundamental group of a square complex…

We bootstrap the $4$-point amplitude of $\mathcal{N}=2$ hypermultiplets in $\text{AdS}_2 \times \text{S}^2$ at tree-level and for arbitrary external weights. We hereby explicitly demonstrate the existence of a hidden four-dimensional…

This paper concerns some novel features of maximal parabolic Eisenstein series at certain special values of their analytic parameter s. These series arise as coefficients in the R4 and D4R4 interactions in the low energy expansion of…

In [1] we have constructed a [n+1/2]+1 parameters family of irreducible representations of the Braid group B_3 in arbitrary dimension using a $q-$deformation of the Pascal triangle. This construction extends in particular results by S.P.…