Related papers: Filtered complexes and cohomologically equivalent …

Let $n$ be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent Hessenberg variety in $GL(n,{\mathbb{C}})/B$ such that its associated graded ring has graded…

There are two de Rham complexes in diffeology. The original one is due to Souriau and the other one is the singular de Rham complex defined by a simplicial differential graded algebra. We compare the first de Rham cohomology groups of the…

The Fr\"olicher spectral sequence of a compact complex manifold $X$ measures the difference between Dolbeault cohomology and de Rham cohomology. We construct for $n\geq 2$ nilmanifolds with left-invariant complex structure $X_n$ such that…

We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences converging to zero whose first pages contain…

We construct a natural filtration on $T(1)$-local $\mathrm{TC}$ for any animated commutative rings using prismatic cohomology and descent theory. In the course of the construction, we also study some general properties of prismatic…

Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-modules to be minimal, in the sense that every self homotopy equivalence is an isomorphism. To do this, we exploit Enochs' description of the…

We prove that the Bredon homology or cohomology of the partition complex with fairly general coefficients is either trivial or computable in terms of constructions with the Steinberg module. The argument involves developing a theory of…

In this paper, we define `simplicial GKM orbifold complexes' and study some of their topological properties. We introduce the concept of filtration of regular graphs and `simplicial graph complexes', which have close relations with…

By Rickard's work, two rings are derived equivalent if there is a tilting complex, constructed from projective modules over the first ring such that the second ring is the endomorphism ring of this tilting complex. In this work I describe,…

Let $R=\Bbbk[x_1,\..., x_n]$ and $M=R^s/I$ a multigraded squarefree module. We discuss the construction of cochain complexes associated to $M$ and we show how to interpret homological invariants of $M$ in terms of topological computations.…

Chen's iterated integrals are treated within synthetic differential geometry. The main result is that iterated integrals produce a subcomplex of the de Rham complex on the free path space as well as based path spaces.

Given an abelian category $\mathcal{A}$ with enough injectives we show that a short exact sequence of chain complexes of objects in $\mathcal{A}$ gives rise to a short exact sequence of Cartan-Eilenberg resolutions. Using this we construct…

The aim of this paper is to present a method for computation of persistent homology that performs well at large filtration values. To this end we introduce the concept of filtered covers. We show that the persistent homology of a bounded…

We investigate deformations of free and linear free divisors. We introduce a complex similar to the de Rham complex whose cohomology calculates deformation spaces. This cohomology turns out to be zero for many linear free divisors and to be…

Using cohomological methods, we prove a criterion for the embedding of a group extension with abelian kernel into the split extension of a co-induced module. This generalises some earlier similar results. We also prove an assertion about…

In this paper we use invariant theory to develop the notion of cohomological detection for Type I classical Lie superalgebras. In particular we show that the cohomology with coefficients in an arbitrary module can be detected on smaller…

We compute symplectic cohomology for Milnor fibres of certain compound Du Val singularities that admit small resolution by using homological mirror symmetry. Our computations suggest a new conjecture that the existence of a small resolution…

For complex parallelisable manifolds $\Gamma\backslash G$, with $G$ a solvable or semisimple complex Lie group, the Fr\"olicher spectral sequence degenerates at the second page. In the solvable case, the de-Rham cohomology carries a pure…

Starting from the axiomatic description of meromorphic functions with prescribed analytic properties, we introduce the cosimplicial cohomology of restricted meromorphic functions defined on foliations of smooth complex manifolds. Spaces for…

We prove an extension of a theorem of A.Ros on a characterization of seven compact Kaehler submanifolds by holomorphic pinching to certain submanifolds of the complex Grassmannian manifolds.