Related papers: Higher spectral sequences
In this paper, we develop a structure theory for generalized spectral sequences, which are derived from chain complexes that are filtered over arbitrary partially ordered sets. Also, a more general construction method reminiscent of exact…
The higher Leray-Serre spectral sequence associated with a tower of fibrations represents a generalization of the classical Leray-Serre spectral sequence of a fibration. In this work, we present algorithms to compute higher Leray-Serre…
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
We describe a variant construction of the unstable Adams spectral the sequence for a space $Y$, associated to any free simplicial resolution of $H^*(Y;R)$ for $R=\mathbb{F}_p$ or $\mathbb{Q}$. We use this construction to describe the…
We study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field. Our method is based on a decomposition of the persistent homology. We demonstrate that, under fairly general…
Given a filtration of a commutative monoid $A$ in a symmetric monoidal stable model category $\mathcal{C}$, we construct a spectral sequence analogous to the May spectral sequence whose input is the higher order topological Hochschild…
We give a very brief introduction to the machinery of spectral sequences, including the spectral sequence of a bicomplex. We then briefly introduce a generalisation of the spectral sequences of a bicomplex to the spectral sequences of…
In this work, we construct a persistent version of the well-known Leray spectral sequence. More precisely, we construct a spectral sequence that computes the persistent cohomology of a space from the persistent cohomology in each open set…
In this work, we build a spectral sequence in motivic homotopy that is analogous to both the Serre spectral sequence in algebraic topology and the Leray spectral sequence in algebraic geometry. Here, we focus on laying the foundations…
The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.
We build a spectral sequence converging to the cohomology of a fusion system with a strongly closed subgroup. This spectral sequence is related to the Lyndon-Hochschild-Serre spectral sequence and coincides with it for the case of an…
This paper introduces a new construction of subcomplexes associated with a truncated multicomplex. Inspired by the machinery of spectral sequences, this construction yields a collection of interrelated subcomplexes whose differentials…
Extending constructions by Gabriel and Zisman, we develop a functorial framework for the cohomology and homology of simplicial sets with very general coefficient systems given by functors on simplex categories into abelian categories.…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
In previous work with Niles Johnson the author constructed a spectral sequence for computing homotopy groups of spaces of maps between structured objects such as G-spaces and E_n-ring spectra. In this paper we study special cases of this…
Let $X$ be the prime spectrum of a ring. In [arXiv:0707.1525] the authors define a topology on $X$ by using ultrafilters and they show that this topology is precisely the constructible topology. In this paper we generalize the construction…
We study homotopy theory of the category of spectral sequences with respect to the class of weak equivalences given by maps which are quasi-isomorphisms on a fixed page. We introduce the category of extended spectral sequences and show that…
Inspired by Rumin's work on a subcomplex in sub-Riemannian manifolds which is cohomologically equivalent to the de Rham complex, we present a more general construction that produces subcomplexes from any filtered cochain complex of finite…
We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…
We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial…