相关论文: Cell-like resolutions preserving cohomological dim…

Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \to H$ with cocompact image. Answering a question of Cornulier, we show…

Let $G$ be a finite abelian group with exponent $n$, and let $r$ be a positive integer. Let $A$ be a $k\times m$ matrix with integer entries. We show that if $A$ satisfies some natural conditions and $|G|$ is large enough then, for each…

We prove that two algebraic embeddings of a smooth variety $X$ in $\mathbb{C}^m$ are the same up to a holomorphic coordinate change, provided that $2 \dim X + 1$ is smaller than or equal to $m$. This improves an algebraic result of Nori and…

We prove that many completeness properties coincide in metric spaces, precompact groups and dense subgroups of products of separable metric groups. We apply these results to function spaces C_p(X,G) of G-valued continuous functions on a…

Let X be a (connected and reduced) complex space. A q-collar of X is a bounded domain whose boundary is a union of a strongly q-pseudoconvex, a strongly q-pseudoncave and two flat (i.e. locally zero sets of pluriharmonic functions)…

Let G be a group which is topologically a CW-complex, BG a classifying space for G, and A a discrete abelian group. To a central extension of G by A, one can associate a cohomology class in $H^2(BG,A)$. We show this association is…

Let $n \geq 1$ be an integer, let $V=(\mathbb{Z}/2\mathbb{Z})^{n}$ and let $X$ be a $V$-CW-complex. If $X$ is a finite $CW$-complexe, the equivariant modulo $2$ cohomology of the $V$-CW-complexe $X$, denoted by $H_{V}^{*}(X,…

As proved by Dimov [Acta Math. Hungarica, 129 (2010), 314--349], there exists a duality L between the category HLC of locally compact Hausdorff spaces and continuous maps, and the category DHLC of complete local contact algebras and…

A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main result characterizes C-rigid complexes. Specialized to the case when C is the relative…

We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log (dim X) = O(log (dim V)) and (2) every…

Suppose $G$ is a connected complex Lie group and $H$ is a closed complex subgroup such that $X := G/H$ is Kaehler and the codimension of the top non-vanishing homology group of $X$ with coefficients in $\mathbb Z_2$ is less than or equal to…

A recent result of M. Kourganoff states that if $D$ is a closed, reducible, non-flat, Weyl connection on a compact conformal manifold $M$, then the universal covering of $M$, endowed with the metric whose Levi-Civita covariant derivative is…

For any k-coalgebra C it is shown that similar quasi-finite C-comodules have strongly equivalent coendomorphism coalgebras; (the converse is in general not true). As an application we give a general result about codepth two coalgebra…

We prove that if $G = G_1\times\dots\times G_n$ acts essentially, properly and cocompactly on a CAT(0) cube complex X, then the cube complex splits as a product. We use this theorem to give various examples of groups for which the minimal…

We show that a compact K\"ahler manifold $M$ containing a smooth connected divisor $D$ such that $M \setminus D$ is a homology cell, e.g., contractible, must be projective space with $D$ a hyperplane, provided $\dim M \not \equiv 3 \pmod…

We prove that $$ \cat X\le cd(\pi_1(X))+\bigg\lceil\frac{\dim X-1}{2}\bigg\rceil$$ for every CW complex $X$ where $cd(\pi_1(X))$ denotes the cohomological dimension of the fundamental group of $X$.

Let k be a complete, non-Archimedean field and let X be a k-analytic space ; assume that there exists a tamely ramified finite extension L/k such that X_L is isomorphic to an open polydisc over L ; we prove that X is itself isomorphic to an…

For an oriented cohomology theory A and a relative cellular space X, we decompose the A-motive of X into a direct sum of twisted motives of the base spaces. We also obtain respective decompositions of the A-cohomology of X. Applying them,…

Let K be a finite extension of Q_p and X a smooth projective variety over K. We define the notion of totally degenerate reduction of such an X and the associated Chow complexes of the special fibre of a suitable regular proper model of X…

Minimal cellular resolutions of the edge ideals of cointerval hypergraphs are constructed. This class of d-uniform hypergraphs coincides with the complements of interval graphs (for the case d=2), and strictly contains the class of…