Related papers: $7$-located locally $5$-large complexes are aspher…

A loop is shown to be a universal Osborn loop if and only if it has a particular simplicial complex. A loop is shown to be a universal Osborn loop and obeys two new identities if and only if it has another particular simplicial complex. A…

In our recent work we described conditions under which a multi-parameter random simplicial complex is connected and simply connected. We showed that the Betti numbers of multi-parameter random simplicial complexes in one specific dimension…

We classify rational cuspidal curves of degrees 6 and 7 in the complex projective plane, up to symplectic isotopy. The proof uses topological tools, pseudoholomorphic techniques, and birational transformations.

In this paper we give the complete classification of $5$-dimensional complex solvable symmetric Leibniz algebras.

This note presents a self-contained proof that acyclic and locally acyclic cluster algebras coincide with their upper cluster algebras.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the $s$-uniform variant of the problem is…

We introduce the notion of locally consistent system of half-spaces for a real hyperplane arrangement. We embed a sphere in the complexified complement by shifting the real unit sphere into the imaginary direction indicated by the…

We prove that numerous negatively curved simply connected locally compact polyhedral complexes, admitting a discrete cocompact group of automorphisms, have automorphism groups which are locally compact, uncountable, non linear and virtually…

We describe the different classes of $\mathrm{Spin(7)}$ structures in terms of spinorial equations. We relate them to the spinorial description of $\mathrm{G}_2$ structures in some geometrical situations. Our approach enables us to analyze…

We prove that certain acyclic cluster algebras over the complex numbers are the coordinate rings of holomorphic symplectic manifolds. We also show that the corresponding quantum cluster algebras have no non-trivial prime ideals. This allows…

We show that a symmetric superposition of five standing plane waves can be expressed as an infinite series of terms of decreasing wavenumber, where each term is a product of five plane waves. We show that this series converges pointwise in…

We introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. They are defined as simply connected prism complexes satisfying some local combinatorial conditions. We study…

We show that compact locally symmetric Lorentz manifolds are geodesically complete.

We show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a $C(9)$ cubical presentation is trivial, and use this to provide classifying spaces for proper actions for the fundamental groups of…

We prove that the pluri-fine topology on any open set $\Omega$ in $\mathbb{C}^{n}$ is locally connected. This answers a question by Fuglede in [4]. See also Bedford [6].

We establish that if $d \geq 2k + 6$ and $q$ is odd and sufficiently large with respect to $\alpha \in (0,1)$, then every set $A\subseteq \mathbf{F}_q^d$ of size $|A| \geq \alpha q^d$ will contain an isometric copy of every spherical…

It is well known that isoperimetric regions in a smooth compact $(n+1)$-manifold are smooth, up to a closed set of codimension at most $6$. In this note, we first construct an $8$-dimensional compact smooth manifold whose unique…

In this paper we prove that a generic rational equation of degree $7$ is solvable by 2-fold origami. In particular we show how to septisect an arbitrary angle. This extends the work of Alperin & Lang and Nishimura on 2-fold origami.…

We give an affirmative answer to a conjecture of Ma. Kato, namely that every compact complex surface $S$ in Kodaira's class $VII_0$ with $b_2(S) > 0$ and $b_2(S)$ rational curves, admits a global spherical shell.

This paper studies cluster algebras locally, by identifying a special class of localizations which are themselves cluster algebras. A `locally acyclic cluster algebra' is a cluster algebra which admits a finite cover (in a geometric sense)…