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We introduce and study, for a process P delivering edges on the Cartesian product of the vertex sets of a given set of graphs, the P-product of these graphs, thereby generalizing many types of product graph. Analogous to the notion of a…
We study the categorical homology of Zappa-Sz\'ep products of small categories, which include all self-similar actions. We prove that the categorical homology coincides with the homology of a double complex, and so can be computed via a…
We establish the foundations of the theory of persistent cohomology operations, derive decomposition formulas for wedge sums and products, and prove their Gromov-Hausdorff stability. We use these results to construct pairs of Riemannian…
The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…
In this paper, we consider the lengths of cycles that can be embedded on the edges of the generalized pancake graphs which are the Cayley graph of the generalized symmetric group $S(m,n)$, generated by prefix reversals. The generalized…
The paper studies the $K$-theoretic invariants of the crossed product $C^{*}$-algebras associated with an important family of homeomorphisms of the tori $\Bbb{T}^{n}$ called {\em Furstenberg transformations}. Using the Pimsner-Voiculescu…
We give a formula for the geometric fixed-points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to…
In this paper, we initiate a systematic study of generalized binomial edge ideals of whisker graphs by working within a substantially broader class of graphs. We extend the notion of generalized corona products, and through this enlarged…
The $n$-th symmetric product of a topological space $X$ is the orbit space of the natural action of the symmetric group $S_n$ on the product space $X^n$. In this paper, we compute the sequential topological complexities of (finite products…
We relate polyhedral products of topological spaces to graph products of groups. The loop homology algebras of polyhedral products are identified with the universal enveloping algebras of the Lie algebras associated with central series of…
A covariant Poisson bracket and an associated covariant star product in the sense of deformation quantization are defined on the algebra of tensor-valued differential forms on a symplectic manifold, as a generalization of similar structures…
We consider a smooth groupoid of the form \Sigma\rtimes\Gamma where \Sigma is a Riemann surface and \Gamma a discrete pseudogroup acting on \Sigma by local conformal diffeomorphisms. After defining a K-cycle on the crossed product…
Stefan and Guichardet have provided Lyndon-Hochschild-Serre type spectral sequences which converge to the Hochschild cohomology and Ext groups of a smash product. We show that these spectral sequences carry natural multiplicative…
We study smooth complex hypersurfaces in direct products of closed hyperbolic Riemann surfaces and give a classification in terms of their fundamental groups. This answers a question of Delzant and Gromov on subvarieties of products of…
Motivated by the study of symmetries of C*-algebras, as well as by multivariate operator theory, we introduce the notion of an SU(2)-equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz-Pimsner…
We define group-twisted Alexander-Whitney and Eilenberg-Zilber maps for converting between bimodule resolutions of skew group algebras. These algebras are the natural semidirect products recording actions of finite groups by automorphisms.…
We build resolutions for general twisted tensor products of algebras. These bimodule and module resolutions unify many constructions in the literature and are suitable for computing Hochschild (co)homology and more generally Ext and Tor for…
The goal of this paper is to first define a Hodge theoretic fundamental group for smooth connected complex algebraic varieties and then prove and study a right exact sequence of Hodge theoretic fundamental groups associated to a smooth…
We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns…
We consider the finite generation property for cohomology algebra of pointed finite tensor categories via de-equivariantization and exact sequence of finite tensor categories. As a result, we prove that all coradically graded pointed finite…