Related papers: Connected simplicial algebras are Andr\'e-Quillen …

We prove that the classical map comparing Adams' cobar construction on the singular chains of a pointed space and the singular cubical chains on its based loop space is a quasi-isomorphism preserving explicitly defined monoidal…

We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…

Given a directed graph E, we construct for each real number l a quiver whose vertex space is the topological realisation of E, and whose edges are directed paths of length l in the vertex space. These quivers are not topological graphs in…

This is the final one in the series of papers where we introduce and study the $C^*$-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated $C^*$-algebras are…

We prove a version of Koszul duality and the induced derived equivalence for Adams connected $A_\infty$-algebras that generalizes the classical Beilinson-Ginzburg-Soergel Koszul duality. As an immediate consequence, we give a version of the…

We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a…

Let $A$ and $C$ be two unital simple C*-algebas with tracial rank zero. Suppose that $C$ is amenable and satisfies the Universal Coefficient Theorem. Denote by ${{KK}}_e(C,A)^{++}$ the set of those $\kappa$ for which…

Given a homomorphism of commutative noetherian rings $\phi: R \to S$, Daniel Quillen conjectured in 1970 that if the Andre-Quillen homology functors $D_n(S|R,-)$ vanish for all $n \gg 0$, then they vanish for all $n \ge 3$. We prove the…

We prove that for any reduced differential graded Lie algebra L, the classical Quillen geometrical realization $\langle L\rangle_Q$ is homotopy equivalent to the realization $\langle L\rangle= Hom_{\bf cdgl}(\mathfrak{L}_\bullet, L)$…

We show that $\tau$-tilting finite simply connected algebras are representation-finite. Then, some related algebras are considered, including iterated tilted algebras, tubular algebras and so on. We also prove that the $\tau$-tilting…

The aim of this paper is to study convergence of Bousfield-Kan completions with respect to the 1-excisive approximation of the identity functor and exotic convergence of the Taylor tower of the identity functor, for algebras over operads in…

If T is an algebraic torus defined over a discretely valued field K with perfect residue field k, we relate the K-cohomology of T to the k-cohomology of certain objects associated to T. When k has cohomological dimension <= 1, our results…

We observe that Beck modules for a commutative monoid are exactly modules over a graded commutative ring associated to the monoid. Under this identification, the Quillen cohomology of commutative monoids is a special case of Andr\'e-Quillen…

We investigate the algebra of an ample groupoid, introduced by Steinberg, over a semifield S. In particular, we obtain a complete characterization of congruence-simpleness for Steinberg algebras of second-countable ample groupoids,…

We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homology of a k-graph coincides with the homology of its topological realisation as…

We introduce a structure termed ``connected cyclic diagonal'' on a chain complex, which induces stable power operations in its cohomology with the property that negative power operations consistently vanish. This chain level structure is…

We identify the obstructions for the functoriality and the uniqueness of the totalization functor, (partially) defined on the category of simplicial objects in the homotopy category of a stable model category, and we use a result from the…

This paper sets up the foundations for derived algebraic geometry, Goerss--Hopkins obstruction theory, and the construction of commutative ring spectra in the abstract setting of operadic algebras in symmetric spectra in an (essentially)…

Using the Harpaz-Nuiten-Prasma interpretation of the Dwyer-Kan-Smith cohomology of a simplicial category $\mathcal{X}$, we obtain a cochain complex for the Andr\'{e}-Quillen cohomology groups in which the $k$-invariants for $\mathcal{X}$…

We make use of the flexibility of infinite-index solutions to the Allen-Cahn equation to show that, given any compact hypersurface $\Sigma$ of R^d, with $d\geq 4$, there is a bounded entire solution of the Allen-Cahn equation on R^d whose…