Related papers: Exponentials of non-singular simplicial sets

Let $H$ be a group acting on a simply-connected diagrammatically reducible combinatorial 2-complex $X$ with fine 1-skeleton. If the fixed point set $X^ H$ is non-empty, then it is contractible. Having fine 1-skeleton is a weaker version of…

The $k$-secant degree is studied with a combinatorial approach. A planar toric degeneration of any projective toric surface $X$ corresponds to a regular unimodular triangulation $D$ of the polytope defining $X$. If the secant ideal of the…

In this article, we prove that a compact open set in the field $\mathbb{Q}_p$ of $p$-adic numbers is a spectral set if and only if it tiles $\mathbb{Q}_p$ by translation, and also if and only if it is $p$-homogeneous which is easy to check.…

We study $h$-vectors of simplicial complexes which satisfy Serre's condition ($S_r$). We say that a simplicial complex $\Delta$ satisfies Serre's condition ($S_r$) if $\tilde H_i(\lk_\Delta(F);K)=0$ for all faces $F \in \Delta$ and for all…

We prove that the set of leaves of a holomorphic lamination of codimension one that are non-transversal to a germ of a holomorphic map is discrete.

We study finite foldable cubical complexes of nonpositive curvature (in the sense of A.D. Alexandrov). We show that such a complex X admits a graph of spaces decomposition. It is also shown that when dim X=3, X contains a closed rank one…

We study a class of signomials whose positive support is the set of vertices of a simplex and which may have several negative support points in the simplex. Various groups of authors have provided an exact characterization for the global…

Many special classes of simplicial sets, such as the nerves of categories or groupoids, the 2-Segal sets of Dyckerhoff and Kapranov, and the (discrete) decomposition spaces of G\'{a}lvez, Kock, and Tonks, are characterized by the property…

Consider a complex one dimensional foliation on a complex surface near a singularity $p$. If $\mathcal{I}$ is a closed invariant set containing the singularity $p$, then $\mathcal{I}$ contains either a separatrix at $p$ or an invariant real…

Let X be a finite set of cardinality n. The Kalmanson complex K_n is the simplicial complex whose vertices are non-trivial X-splits, and whose facets are maximal circular split systems over X. In this paper we examine K_n from three…

We refer to the set of the orders of elements of a finite group as its spectrum and say that groups are isospectral if their spectra coincide. We prove that with the only specific exception the solvable radical of a nonsolvable finite group…

Let $X_{\bullet}$ denote a simplicial space. The purpose of this note is to record a decomposition of the suspension of the individual spaces $X_n$ occurring in $X_{\bullet}$ in case the spaces $X_n$ satisfy certain mild topological…

We show that for each countable simplicial complex P the following conditions are equivalent: (1) $P \in AE(X)$ iff $P \in AE(\beta X)$ for any space X; (2) There exists a P-invertible map of a metrizable compactum X with $P \in AE(X)$ onto…

If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in (X,Y) has a normal hyperdefinable X-internal subgroup N such that G/N is Y-internal; N is unique up to commensurability. In order to make…

We generalize a theorem of Delzant classifying compact connected symplectic manifolds with completely integrable torus actions to certain singular symplectic spaces. The assumption on singularities is that if they are not finite quotient…

The prime simplicial complex $\Pi(G)$ of a finite group $G$ is composed of all sets of primes $S$ where $G$ has an element of order the product of primes in $S$, with the subsets partially ordered by inclusion. This complex was introduced…

In 2017, Walter Taylor showed that there exist $2$-dimensional simplicial complexes which admit the structure of topological modular lattice but not topological distributive lattice. We give a positive answer to his question as to whether…

We classify multidimensionally consistent maps given by (formal or convergent) series of the following kind: $$ T_k x_{ij}=x_{ij} + \sum_{m=2}^\infty A_{ij ; \, k}^{(m)}(x_{ij},x_{ik},x_{jk}), $$ where $A_{ij;\, k}^{(m)}$ are homogeneous…

We prove that if $\pi$ is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are $\pi$-groups. In particular, when $\pi$ is the empty set, we obtain Henckell's decidability of…

We classify finite groups in which the centralisers of certain non-central elements are soluble. This includes a full structural description of groups whose non-central element centralisers are all soluble, and a reduction theorem for the…