Related papers: Polyhedral products for shifted complexes and high…

In this work we propose composition products in the class of complex harmonic functions so that the composition of two such functions is again a complex harmonic function. From here we begin the study of the iterations of the functions of…

In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted…

In this paper we obtain improved dimensional thresholds for dot product sets corresponding to compact subsets of a paraboloid. As a direct application of these estimates, we obtain significant improvements to the best known dimensional…

Let $P$ be a closed convex cone in $\mathbb{R}^{n}$. Assume that $P$ is spanning i.e. $P-P=\mathbb{R}^{n}$ and pointed i.e. $P \cap -P=\{0\}$. Let $\alpha:=\{\alpha_{x}:x \in P\}$ be a $\sigma$-weakly continuous family of unital normal…

We study when an additive mapping preserving orthogonality between two complex inner product spaces is automatically complex-linear or conjugate-linear. Concretely, let $H$ and $K$ be complex inner product spaces with dim$(H)\geq 2$, and…

In this paper, we prove a dihedral extremality and rigidity theorem for a large class of codimension zero submanifolds with polyhedral boundary in warped product manifolds. We remark that the spaces considered in this paper are not…

We study the C$^*$-algebra of Wiener-Hopf operators $A_\Omega$ on a cone $\Omega$ with polyhedral base $P$. As is known, a sequence of symbol maps may be defined, and their kernels give a filtration by ideals of $A_\Omega$, with liminary…

Warped products are one of the simplest families of Riemannian manifolds that can have non-trivial geometries. In this article, we characterize the geometry of hypersurface embeddings arising from warped product manifolds using the language…

In this paper, we compute the homology group and cohomology algebra of various polyhedral product objects uniformly from the point of view of diagonal tensor product. As applications, we introduce the polyhedral product method into…

The Hochschild cohomology of a tensor product of algebras is isomorphic to a graded tensor product of Hochschild cohomology algebras, as a Gerstenhaber algebra. A similar result holds when the tensor product is twisted by a bicharacter. We…

We show that the bigraded quasi-isomorphism type of the bigraded, bidifferential algebra of forms on a compact K\"ahler manifold generally contains more information than the de Rham cohomology algebra with its real Hodge structure. More…

We study the C*-algebra crossed product $C_0(X)\rtimes G$ of a locally compact group $G$ acting properly on a locally compact Hausdorff space $X$. Under some mild extra conditions, which are automatic if $G$ is discrete or a Lie group, we…

For a space X acted by a finite group $\G$, the product space $X^n$ affords a natural action of the wreath product $\Gn$. In this paper we study the K-groups $K_{\tG_n}(X^n)$ of $\Gn$-equivariant Clifford supermodules on $X^n$. We show that…

Let $\mathfrak{g}$ be a Leibniz algebra and $E$ a vector space containing $\mathfrak{g}$ as a subspace. All Leibniz algebra structures on $E$ containing $\mathfrak{g}$ as a subalgebra are explicitly described and classified by two…

We show that for any face $F$ of a simple polytope $P$ the canonical equivariant homeomorphisms $h_P:\,\mathcal Z_P\to\mathcal Z_{K_P}$ and $h_F:\,\mathcal Z_F\to\mathcal Z_{K_F}$ are linked in a pentagonal commutative diagram with the maps…

We characterize the sets $\XX$ of all products $PQ$, and $\YY$ of all products $PQP$, where $P,Q$ run over all orthogonal projections and we solve the problems $\arg\min\{\|P-Q\|: (P,Q) \in \cal Z\}$, for $\cal Z=\XX$ or $\YY.$ We also…

In this paper we study \emph{threefolds isogenous to a product of mixed type} i.e. quotients of a product of three compact Riemann surfaces $C_i$ of genus at least two by the action of a finite group $G$, which is free, but not diagonal. In…

The problem of existence of nontrivial Massey products in cohomology of a space is well-known in algebraic topology and homological algebra. A number of problems in complex geometry, symplectic geometry, and algebraic topology can be stated…

We describe locally the representation varieties of fundamental groups for smooth complex varieties at representations coming from the monodromy of a variation of mixed Hodge structure. Given such a manifold $X$ and such a linear…

To factorize and to decompose the graphs of representative functions on the free monoid X * (generated by the alphabet X ) with values in the ring A containing Q, we examine various products of series (as concatenation, shuffle and its…