Related papers: A spectral sequence for fusion systems

We generalize recent developments on normal forms and the spectral sequences method to make a foundation for parametric normal forms. We further introduce a new style and costyle to obtain unique parametric normal forms. The results are…

In this paper, we construct a seven-term exact sequence involving the cohomology groups of a group extension. Although the existence of such a sequence can be derived using spectral sequence arguments, there is little knowledge about some…

This paper explains the theory of spectral sequences via d\'ecalage and the Beilinson t-structure.

Working in the context of symmetric spectra, we describe and study a homotopy completion tower for algebras and left modules over operads in the category of modules over a commutative ring spectrum (e.g., structured ring spectra). We prove…

Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety of potential applications in particular in optics and photonics. However, the experimental realization is…

Let G be group; a finite p-subgroup S of G is a Sylow p-subgroup if every finite p-subgroup of G is conjugate to a subgroup of S. In this paper, we examine the relations between the fusion system over S which is given by conjugation in G…

When identified with sequences of irreducible Hermitian-Einstein connections, sequences of stable holomorphic bundles of fixed topological type and bounded degree on a compact complex surface equipped with a Gauduchon metric are shown to…

The Leray-Serre and the Eilenberg-Moore spectral sequences are fundamental tools for computing the cohomology of a group or, more generally, of a space. We describe the relationship between these two spectral sequences when both of them…

In this paper, we introduce a symmetric continuous cohomology of topological groups. This is obtained by topologizing a recent construction due to Staic (J. Algebra 322 (2009), 1360-1378), where a symmetric cohomology of abstract groups is…

Cohomology of Specht modules for the symmetric group can be equated in low degrees with corresponding cohomology for the Borel subgroup B of the general linear group GL_d(k), but this has never been exploited to prove new symmetric group…

We develop a theory of R-module Thom spectra for a commutative symmetric ring spectrum R and we analyze their multiplicative properties. As an interesting source of examples, we show that R-algebra Thom spectra associated to the special…

In this paper we define the closure under weak convergence of the class of p-tempered {\alpha}-stable distributions. We give necessary and sufficient conditions for convergence of sequences in this class. Moreover, we show that any element…

We extend Homotopy Type Theory with a novel modality that is simultaneously a monad and a comonad. Because this modality induces a non-trivial endomap on every type, it requires a more intricate judgemental structure than previous modal…

We construct and analyze the "syntomic Steenrod algebra", which acts on the mod $p$ syntomic cohomology (also known as etale-motivic cohomology) of algebraic varieties in characteristic $p$. We then apply the resulting theory to resolve the…

We introduce the notion of compatible actions in the context of split extensions of finite dimensional Lie algebras over a field. Using compatible actions, we construct a new resolution to compute the cohomology of semi-direct products of…

Tate sequences are an important tool for tackling problems related to the (ill-understood) Galois structure of groups of $S$-units. The relatively recent Tate sequence "for small $S$" of Ritter and Weiss allows one to use the sequence…

The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open…

Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…

A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…

We extend Dwyer's sharp subgroup homology decomposition of the classifying space of a finite group to arbitrary saturated fusion systems and arbitrary Mackey functors.