Related papers: Presentation complexes with the fixed point proper…

We prove that a 2n-dimensional compact homogeneous nearly Kahler manifold with strictly positive sectional curvature is isometric to CP^{n}, equipped with the symmetric Fubini-Study metric or with the standard Sp(m)-homogeneous metric, n…

In this work we prove constructively that the complement ${\mathbb R}^n\setminus{\mathcal K}$ of an $n$-dimensional unbounded convex polyhedron ${\mathcal K}\subset{\mathbb R}^n$ and the complement ${\mathbb R}^n\setminus{\rm Int}({\mathcal…

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in…

We demonstrate the homogeneity of the Hilbert Cube. In particular, we construct explicit self-homeomorphisms of the Hilbert cube so that given any two points, a homeomorphism moving one to the other may be realized.

A well-known result says that the Euclidean unit ball is the unique fixed point of the polarity operator. This result implies that if, in $\mathbb{R}^n$, the unit ball of some norm is equal to the unit ball of the dual norm, then the norm…

We first notice in this article that if a compact K\"{a}hler manifold has the same integral cohomology ring and Pontrjagin classes as the complex projective space $\mathbb{C}P^n$, then it is biholomorphic to $\mathbb{C}P^n$ provided $n$ is…

A celebrated theorem of Hadwiger states that the Euler-Poincar\'e characteristic is the the unique invariant and continuous valuation on the distributive lattice of compact polyhedra in R^n that assigns value one to each convex non-empty…

We establish fixed-point theorems for Meir-Keeler-type contractions in b-metric spaces. While Lu et al. demonstrated via an explicit counterexample that classical Meir-Keeler contractions may fail to admit fixed points in this setting, we…

We show that the following conditions on a C*-algebra are equivalent: (i) it has the fixed point property for nonexpansive mappings, (ii) the spectrum of every self adjoint element is finite, (iii) it is finite dimensional. We prove that…

The question, under what geometric assumptions on a space X an n-quasiflat in X implies the existence of an n-flat therein, has been investigated for a long time. It was settled in the affirmative for Busemann spaces by Kleiner, and for…

We introduce a large scale analogue of the classical fixed-point property for continuous maps, which shall apply to coarse maps. We also develop a coarse version of degree for coarse maps on Euclidean spaces. Then, applying a coarse…

We provide a natural interpretation of the secondary Euler characteristic and introduce higher Euler characteristics. For a compact oriented manifold of odd dimension, the secondary Euler characteristic recovers the Kervaire…

We investigate the algebraicity of compact K\"ahler manifolds admitting a positive rational Hodge class of bidimension $(1,1)$. We prove that if the dual K\"ahler cone of a compact K\"ahler manifold $X$ contains a rational class as an…

We prove that the Newton product of efficient polynomial projectors is still efficient. Various polynomial approximation theorems are established involving Newton product projectors on spaces of holomorphic functions on a neighborhood of a…

Geometry of buildings is used to prove some homological properties of the category of smooth representations of a reductive p-adic group (Kazhdan's "pairing conjecture", Bernstein's description of homological duality in terms of…

We establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by simplicial isometries on finite rank buildings with measurable…

In this paper, we first construct $k$-dimensional compact complex manifolds from automorphisms of $\mathbb{C}^k$ which admit a fixed attracting point at infinity. Then, we charactize the fundamental group as well as the universal covering…

The study of comparison theorems in geometry has a rich history. In this paper, we establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by…

Margot (1994) in his doctoral dissertation studied extended formulations of combinatorial polytopes that arise from "smaller" polytopes via some composition rule. He introduced the "projected faces property" of a polytope and showed that…

This note which can be viewed as a complement to Alex Postnikov's paper math.CO/0507163, presents a self-contained overview of basic properties of nested complexes and their two dual polyhedral realizations: as complete simplicial fans, and…