Related papers: Homological dimension and dimensional full-valuedn…

Classical Hamming graphs are Cartesian products of complete graphs, and two vertices are adjacent if they differ in exactly one coordinate. Motivated by connections to unitary Cayley graphs, we consider a generalization where two vertices…

We give a survey of our recent results on homological properties of K"othe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of K"othe algebras are also…

We investigate the relationship between smoothness and the relative global dimension of a ring extension. We prove that a smooth commutative algebra $A$ over $B$ has finite relative global dimension $\text{gdim}(A,B)$. Conversely, under a…

In this paper we provide a criteria for geometric finiteness of Kleinian groups in general dimension. We formulate the concept of conformal finiteness for Kleinian groups in space of dimension higher than two, which generalizes the notion…

We show that the main homological dimensions of the algebra of analytic functionals on a connected complex Lie group, as well as some of its completions, coincide with the dimension of the simply connected solvable factor in the canonical…

In this paper we build off of Takahashi and White's $\mathcal{P}_C$-projective dimension and $\mathcal{I}_C$-injective dimension to define these dimensions for when $C$ is a semidaulizing complex. We develop the framework for these…

We study the relation type question, raised by C. Huneke, which asks whether for a complete equidimensional local ring R there exists a uniform bound for the relation type of parameter ideals. Wang gave a positive answer to this question…

Arone and the second author showed that when the dimensions are in the stable range, the rational homology and homotopy of the high dimensional anologues of spaces of long knots can be calculated as the homology of a direct sum of finite…

We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…

We show that the sum of the local cohomological dimension and the rectified $\mathbb Q$-homological depth of a closed analytic subspace of a complex manifold coincide with the dimension of the ambient manifold. The local cohomological…

Let X be a Stein manifold, and let Y be a closed complex submanifold of X. Denote by O(X) the algebra of holomorphic functions on X. We show that the weak (i.e., flat) homological dimension of O(Y) as a Fr'echet O(X)-module equals the…

A monoid presentation is called special if the right-hand side of each defining relation is equal to 1. We prove results which relate the two-sided homological finiteness properties of a monoid defined by a special presentation with those…

We introduce relative preresolving subcategories and precoresolving subcategories of an abelian category and define homological dimensions and codimensions relative to these subcategories respectively. We study the properties of these…

We classify complete curvature homogeneous metrics on simply connected four dimensional manifolds which are invariant under a cohomogeneity one action. We show that they are either isometric to a symmetric space with one of its…

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…

M. Goresky and R. MacPherson intersection homology is also defined from the singular chain complex of a filtered space by H. King, with a key formula to make selections among singular simplexes. This formula needs a notion of dimension for…

We prove that for any field k of characteristic p>0, any separated scheme X of finite type over k, and any overconvergent F-isocrystal E over X, the rigid cohomology H^i(X, E) and rigid cohomology with compact supports H^i_c(X,E) are finite…

We show that Iacob-Iyengar's answer to a question of Avromov-Foxby extends from Noetherian to coherent rings. In particular, a coherent ring R is regular if and only if the injective (resp. projective) dimension of each complex X of…

Let $(X,g)$ be a compact Riemannian stratified space with simple edge singularity. Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a lower dimensional compact smooth manifold. We calculate the various…

We compare singular homology and homology via integral currents in metric spaces that are homeomorphic to smooth manifolds. For such spaces, we provide sufficient conditions that guarantee the existence of a surjective homomorphism from the…