Related papers: The collapse of the periodicity sequence in the st…

Conjecture F from [VW12] states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. We prove a generalization of this conjecture to the…

In the paper we describe complexes whose homologies are naturally isomorphic to the first term of the Vassiliev spectral sequence computing (co)homology of the spaces of long knots in R^d, d>=3. The first term of the Vassiliev spectral…

The paper deals with periodic homogenization of nonlocal symmetric convolution type operators in $L^2(\mathbb R^d)$, whose kernel is the product of a density that belongs to the domain of attraction of an $\alpha$-stable law and a rapidly…

The paper deals with $\Sigma-$composition and $\Sigma$-essential composition of terms, which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids…

Let Y be a random d-dimensional subcomplex of the (n-1)-dimensional simplex S obtained by starting with the full (d-1)-dimensional skeleton of S and then adding each d-simplex independently with probability p=c/n. We compute an explicit…

We introduce new formulations of aperiodicity and cofinality for finitely aligned higher-rank graphs \Lambda, and prove that C*(\Lambda) is simple if and only if \Lambda is aperiodic and cofinal. The main advantage of our versions of…

Let $\mathbf{k}$ be an algebraically closed field of characteristic $\geq 7$ or zero. Let $\mathcal{A}$ be a tame order of global dimension $2$ over a normal surface $X$ over $\mathbf{k}$ such that…

We show the topological Hochschild homology spectrum of a twisted group algebra $\THH(A^{\tau}[G])$ is the Thom spectrum associated to a parametrized orthogonal spectrum $E(A,G)$. We then analyze the structure of the parametrized orthogonal…

We study the cohomology of symbolic dynamical systems called homshifts: they are the nearest-neighbour $\mathbb{Z}^d$ shifts of finite type whose adjacency rules are the same in every direction. Building on the work of Klaus Schmidt…

Let H be a graded Hecke algebra with complex deformation parameters and Weyl group W. We show that the Hochschild, cyclic and periodic cyclic homologies of H are all independent of the parameters, and compute them explicitly. We use this to…

We study equivalences of the form $\Sigma^{V}X\simeq \Sigma^{W}X$, where $G$ is a compact Lie group, $X$ is a $G$-spectrum, and $V$ and $W$ are $G$-representations. These equivalences encode a periodicity phenomenon in $G$-equivariant…

We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted…

Let $\mathfrak{g}$ be an untwisted affine Lie algebra with associated Weyl group $W_a$. To any level 0 weight $\gamma$ we associate a weighted graph $\Gamma_\gamma$ that encodes the orbit of $\gamma$ under the action $W_a$. We show that the…

In this paper, we give an explicit description about the second Hochschild cohomology groups of bipartite Brauer graph algebras with trivial grading. Based on this, we provide geometric interpretations of deformations associated to some…

Let S be an essentially smooth scheme over a field of characteristic exponent c. Let MGL and HZ denote the algebraic cobordism spectrum and the motivic cohomology spectrum over S, respectively. We show that the canonical map MGL/(a1, a2,…

We consider a one-parameter family of piecewise isometries of a rhombus. The rotational component is fixed, and its coefficients belong to the quadratic number field $K=\mathbb{Q}(\sqrt{2})$. The translations depend on a parameter $s$ which…

We prove that the completed cohomology groups of SL_N(Z) in fixed degree stabilize as N goes to infinity. We also prove that the action of Hecke operators on stable cohomology is trivial, in a precisely defined sense.

We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group $\Gamma$. Under favorable conditions, the cohomology is freely generated in a single degree over this graded…

We use algebraic arc complexes to prove a homological stability result for symplectic groups with slope 2/3 for rings with finite unitary stable rank. Symplectic groups are here interpreted as the automorphism groups of formed spaces with…

The Hochschild and (cotriple) cyclic homologies of crossed modules of (not-necessarily-unital) associative algebras are investigated. Wodzicki's excision theorem is extended for inclusion crossed modules in the category of crossed modules…