Related papers: Endpoint-homogeneous fans
For a connected finite poset $P$, let $E(P)$ be the poset induced by the extremal points of $P$. We show that the fixed point property of $E(P)$ implies the fixed point property of $P$. On the other hand, we show that a homomorphism $f :…
In dimension 4, we extend the correspondence between compact nonsingular toric varieties and regular fans to a correspondence between almost complex torus manifolds and families of multi-fans in a geometric way, where an (almost) complex…
Suppose $G$ is a finitely generated infinite group, and $\mathcal G$ is a graph of groups decomposition of $G$ such that the edge groups are finite. This paper establishes that the topology of the Floyd boundary of $G$ is uniquely…
A structure is called homogeneous if every isomorphism between finite substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Ne\v{s}et\v{r}il introduced a relaxed version of homogeneity:…
The category of (abstract) fans is to the category of monoids what the category of schemes is to the category of rings: a fan is obtained by gluing spectra of monoids along open embeddings. Here we study the basic algebraic geometry of…
The goal of this paper is to show that the local Gr\"obner fan is a polyhedral fan for ideals in the ring of power series and the homogenized ring of analytic differential operators. We will also discuss about relations between the local…
We prove that the Chow ring of any simplicial fan is isomorphic to the middle degree part of the tropical cohomology ring of its canonical compactification. Using this result, we prove a tropical analogue of Kleiman's criterion of ampleness…
We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…
Let $t_1,\ldots,t_n$ be $\ell$-group terms in the variables $X_1,\ldots,X_m$. Let $\hat t_1,\ldots,\hat t_n$ be their associated piecewise homogeneous linear functions. Let $G $ be the $\ell$-group generated by $\hat t_1, \ldots,\hat t_n$…
Motivated by definitions in mixed Hodge theory, we define the weight filtration and the monodromy weight filtration on the combinatorial intersection cohomology of a fan. These filtrations give a natural definition of the multivariable…
A graph $G$ is called \emph{claw-o-heavy} if every induced claw ($K_{1,3}$) of $G$ has two end-vertices with degree sum at least $|V(G)|$ in $G$. For a given graph $R$, $G$ is called \emph{$R$-f-heavy} if for every induced subgraph $H$ of…
A homeomorphism of a compact metric space is {\em tight} provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every $C^{1+\alpha}$ diffeomorphism of a closed surface…
A graph is \emph{fan-crossing free} if it has a drawing in the plane so that each edge is crossed by independent edges, that is the crossing edges have distinct vertices. On the other hand, it is \emph{fan-crossing} if the crossing edges…
Let $E$ be a linear space and suppose that $A$ is the global attractor of either (i) a homeomorphism $F:E\rightarrow E$ or (ii) a semigroup $S(\cdot)$ on $E$ that is injective on $A$. In both cases $A$ has trivial shape, and the dynamics on…
In this paper we show that every homeomorphism of the plane with the topological shadowing property has a fixed point. Also, we show that a linear isomorphism of an Euclidean space has the topological shadowing property if and only if the…
For a smooth curve $B$ over an algebraically closed field $k$, for every $B$-flat complete intersection $X_B$ in $B\times_{\text{Spec}\ k} \mathbb{P}^n_k$ of type $(d_1,\dots,d_c)$, if the Fano index is $\geq 2$ and if…
The theta--fan F_theta is the quotient space obtained by identifying the non--isolated points of the product theta \times (omega+1) with a single point \infty. (Here, theta has the discrete topology and omega+1 has the order topology.) We…
A famous construction of Gelfand, Kapranov and Zelevinsky associates to each finite point configuration $A \subset \mathbb{R}^d$ a polyhedral fan, which stratifies the space of weight vectors by the combinatorial types of regular…
We show that finite-type surfaces are characterized by a topological analog of the Hopf property. Namely, an oriented surface $\Sigma$ is of finite-type if and only if every proper map $f\colon\Sigma\to \Sigma$ of degree one is homotopic to…
Following the argument for diffeomorphisms by Galatius and Randal-Williams, we prove that homeomorphisms of 1-connected manifolds of even dimension at least 6 exhibit homological stability. We deduce similar results for PL homeomorphisms…