相关论文: Exactness and stability in homotopical algebra

We define a basic class of algebras which we call homotopy path algebras. We find that such algebras always admit a cellular resolution and detail the intimate relationship between these algebras, stratifications of topological spaces, and…

We show that there is a stable homotopy theory of profinite spaces and use it for two main applications. On the one hand we construct an \'etale topological realization of the stable motivic homotopy theory of smooth schemes over a base…

We study the interplay between the notions of $n$-coherent rings and finitely $n$-presented modules, and also study the relative homological algebra associated to them. We show that the $n$-coherency of a ring is equivalent to the thickness…

Unlike Grothendieck's \'etale fundamental group, Nori's fundamental group does not fulfill the homotopy exact sequence in general. We give necessary and sufficient conditions which force exactness of the sequence.

We introduce the concept of finitely coloured equivalence for unital *-homomorphisms between C*-algebras, for which unitary equivalence is the 1-coloured case. We use this notion to classify *-homomorphisms from separable, unital, nuclear…

One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…

We show a first rectification result for homotopy chain coalgebras over a field. On the one hand, we consider the $\infty$-category obtained by localizing differential graded coalgebras over an operad with respect to quasi-isomorphisms; on…

Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on…

Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…

Highly localized kernels based on orthogonal polynomials have been studied and utilized over several regular domains. Much of the results deduced via these kernels can be treated uniformly in the framework of localizable spaces of…

In 2002, Biss investigated on a kind of fibration which is called rigid covering fibration (we rename it by rigid fibration) with properties similar to covering spaces. In this paper, we obtain a relation between arbitrary topological…

We establish a braid of interlocking exact sequences containing the group of homotopy self-equivalences of a smooth or topological 4-manifold. The braid is computed for manifolds whose fundamental group is finite of odd order.

We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for…

Let $R$ be a commutative ring with unit. We consider the homotopy theory of the category of spectral sequences of $R$-modules with the class of weak equivalences given by those morphisms inducing a quasi-isomorphism at a certain fixed page.…

Our objective in this article is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of the (say) simplicial set embedded in a finite dimensional vector space…

In this note, we prove that the homotopy sequence of the algebraic fundamental group is exact if the base field is of characteristic 0.

The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy…

Connections on a trivial bundle MxG can be identified with their holonomy maps, i.e. with homomorphisms of a groupoid of paths in M into the gauge group G. For a connected compact G, various algebras depending on the set of the smooth…

Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as…

We consider tracial stability, which requires that tuples of elements of a C*-algebra with a trace that nearly satisfy the relation are close to tuples that actually satisfy the relation. Here both "near" and "close" are in terms of the…