Related papers: On Null-homology and stationary sequences
For commutative algebras there are three important homology theories, Harrison homology, Andre-Quillen homology and Gamma-homology. In general these differ, unless one works with respect to a ground field of characteristic zero. We show…
Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration…
We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric stable non-Gaussian discrete-parameter random field using the framework of Hult and Samorodnitsky (2010). Depending on the ergodic…
We define an Artin stack which may be considered as a substitute for the non-existing (or empty) moduli space of stable two-pointed curves of genus zero. We show that this Artin stack can be viewed as the first term of a cyclic operad in…
These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequence and the C-cohomology, including the formulation in…
Let M be an open, connected manifold. A classical theorem of McDuff and Segal states that the sequence of configuration spaces of n unordered, distinct points in M is homologically stable with coefficients in Z: in each degree, the integral…
We prove that the homology of the mapping class groups of non-orientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain that the classifying space of the stable…
The paper is devoted to a generalized and improved version of author's approach to Gromov bounded cohomology theory. In particular, the awkward countability assumption is removed and the aspects related to homological algebra are clarified.…
We generalise a fundamental graph-theoretical fact, stating that every element of the cycle space of a graph is a sum of edge-disjoint cycles, to arbitrary continua. To achieve this we replace graph cycles by topological circles, and…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
This paper deals with measurable stationary symmetric stable random fields indexed by R^d and their relationship with the ergodic theory of nonsingular R^d-actions. Based on the phenomenal work of Rosinski(2000), we establish extensions of…
The goal of this article is to prove the comparison theorem between algebraic and topological nearby cycles of a morphism without slopes. We prove in particular that for a family of holomorphic functions without slopes, if we iterate…
Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a…
In the strong noise regime, we study the homogeneization of quantum trajectories i.e. stochastic processes appearing in the context of quantum measurement. When the generator of the average semi-group can be separated into three distinct…
The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately…
A stationary random sequence admits under some assumptions a representation as the sum of two others: one of them is a martingale difference sequence, and another is a so-called coboundary. Such a representation can be used for proving some…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
For a Markov chain $Y$ with values in a Polish space, consider the entrance chain, obtained by sampling $Y$ at the moments when it enters a fixed set $A$ from its complement $A^c$. Similarly, consider the exit chain, obtained by sampling…
Interactions in complex systems are widely observed across various fields, drawing increased attention from researchers. In mathematics, efforts are made to develop various theories and methods for studying the interactions between spaces.…
This paper applies the decomposition theorem in intersection cohomology to geometric invariant theory quotients, relating the intersection cohomology of the quotient to that of the semistable points for the action. Suppose a connected…