Related papers: Postnikov Invariants of Crossed Complexes
We compare the description of the M-theory form fields via cohomotopy versus that via integral cohomology. The conditions for lifting the latter to the former are identified using obstruction theory in the form of Postnikov towers, where…
Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in which the ambient vector space is acted on by either a unitary…
We define inductively a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the Pi-algebra \pi_* X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology…
We show that for a gradable finite dimensional algebra the perfect complexes and bounded derived category cannot be distinguished by homotopy invariants.
In this paper we study a filtered "K-theoretical" analog of a graded algebra associated to any loopless graph G which was introduced in \cite{PS}. We show that two such filtered algebras are isomorphic if and only if their graphs are…
We describe a general method for algorithmic construction of G-equivariant chain homotopy equivalences from non-equivariant ones. As a consequence, we obtain an algorithm for computing equivariant (co)homology of Eilenberg-MacLane spaces…
We characterize H-spaces which are p-torsion Postnikov pieces of finite type by a cohomological property together with a necessary acyclicity condition. When the mod p cohomology of an H-space is finitely generated as an algebra over the…
The interaction between combinatorics and algebraic and differential geometry is very strong. While researching a problem of Hessian topology, we came across a series of identities of binomial coefficients, which are useful for proving a…
We define a variant of intersection space theory that applies to many compact complex and real analytic spaces $X$, including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to…
Postnikov constructed a decomposition of a totally nonnegative Grassmannian into positroid cells. We provide combinatorial formulas that allow one to decide which cell a given point belongs to and to determine affine coordinates of the…
We show that cellular approximations of nilpotent Postnikov stages are always nilpotent Postnikov stages, in particular classifying spaces of nilpotent groups are turned into classifying spaces of nilpotent groups. We use a modified…
We compare the classical approach of constructing finite Postnikov systems by k-invariants and the global approach of Dwyer, Kan, and Smith. We concentrate on the case of 3-stage Postnikov pieces and provide examples where a classification…
This note which can be viewed as a complement to Alex Postnikov's paper math.CO/0507163, presents a self-contained overview of basic properties of nested complexes and their two dual polyhedral realizations: as complete simplicial fans, and…
In this paper we show that a simplicial complex can be determined uniquely up to isomorphism by its barycentric subdivision or comparability graph. At the end, it is summarized several algebraic, combinatorial and topological invariants of…
This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…
We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of noncommutative index theory of operator algebras. In…
Let p be a singular point of a variety. Consider a resolution where the preimage of p is a simple normal crossing divisor E. The combinatorial structure of E is described by a cell complex D(E), called the dual graph or dual complex of E.…
We study the homotopy theory of diagrams of chain complexes over a field indexed by a finite poset, and show that it can be completely described in terms of appropriate diagrams of graded vector spaces.
We give two equivalent sets of invariants which classify pairs of coisotropic subspaces of finite-dimensional Poisson vector spaces. For this it is convenient to dualize; we work with pairs of isotropic subspaces of presymplectic vector…
We introduce homotopical variants of the axioms of countable and dependent choice for infinity-topoi and use them to give criteria for Postnikov completeness, revisiting a result of Mondal and Reinecke.