Related papers: Fixed Point Sets in Diagrammatically Reducible Com…

A point of a digital space is called simple if it can be deleted from the space without altering topology. This paper introduces the notion simple set of points of a digital space. The definition is based on contractible spaces and…

We give a short and uniform proof of a special case of Tits' Centre Conjecture using a theorem of J-P. Serre and a result from our earlier work. We consider fixed point subcomplexes $X^H$ of the building $X = X(G)$ of a connected reductive…

This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of solutions snapshots, what…

Suppose that $X=G/K$ is the quotient of a locally compact group by a closed subgroup. If $X$ is locally contractible and connected, we prove that $X$ is a manifold. If the $G$-action is faithful, then $G$ is a Lie group.

Let $\mathbbm{P}^{1,an}$ be the Berkovich projective line over a complete, algebraically closed, non-Archimedean field. Let $\phi$ be a degree $\geq 2$ rational map with potential good reduction, acting on $\mathbbm{P}^{1,an}$. In this…

For each finite ordinal n, and each locally-finite group G of cardinality aleph-sub-n, we construct an (n+1)-dimensional, contractible CW-complex on which G acts with finite stabilizers. We use the complex to obtain information about…

In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results…

For which groups G is it true that whenever we form a direct limit of G-sets, dirlim_{i\in I} X_i, the set of its fixed points, (dirlim_I X_i)^G, can be obtained as the direct limit dirlim_I(X_i^G) of the fixed point sets of the given…

Fixed points of $N$ coupled Virasoro minimal models have recently been argued to provide large classes of compact unitary CFTs with $c>1$ and only Virasoro chiral symmetry. In this paper, we vastly increase the set of such potential…

A subset $B \subset Y$ is constructible if it is an element of the smallest family that contains all open sets and is stable under finite intersections and complements. A function $f : X \to Y$ is said to be piece-wise closed if $X$ can be…

Let $X$ be an irreducible, reduced complex projective hypersurface of degree $d$. A point $P$ not contained in $X$ is called uniform if the monodromy group of the projection of $X$ from $P$ is isomorphic to the symmetric group $S_d$. We…

We show that the triangulations of a finite point set form a flip graph that can be embedded isometrically into a hypercube, if and only if the point set has no empty convex pentagon. Point sets of this type include convex subsets of…

We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere. The…

In this paper, the existence of coincidence points and common fixed points for multivalued mappings satisfying certain graphic {\psi}-contraction contractive conditions with set-valued domain endowed with a graph, without appealing to…

In this paper, we study the existence of fixed points for mappings defined on complete (compact) metric space (X, d) satisfying a general contractive (contraction) inequality depended on another function. These conditions are analogous to…

In this article, we characterize the distortion elements of the group of smooth diffeomorphisms of the circle and of the group of compactly supported smooth diffeomorphisms of the real line. More precisely, we prove that, in this context,…

We consider the action of $p$-toral subgroups of $U(n)$ on the unitary partition complex $\mathcal L_n$. We show that if $H\subseteq U(n)$ is $p$-toral and has noncontractible fixed points on $\mathcal L_n$, then the image of $H$ in the…

We exhibit finitely generated torsion-free groups for which any action on any finite-dimensional CW-complex with finite Betti numbers has a global fixed point.

We prove that any unicritical polynomial $f_c:z\mapsto z^d+c$ which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies that the connectedness locus (the ``Multibrot set'') is…

We introduce the notion of weakly systolic complexes and groups, and initiate regular studies of them. Those are simplicial complexes with nonpositive-curvature-like properties and groups acting on them geometrically. We characterize weakly…