Related papers: Decomposition of exact pfd persistence bimodules
We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $\lambda$, and generalize this characterization to cubic real polynomial maps,…
In this note, we establish conditions under which the union of an increasing sequence of completely decomposable modules over domains are again completely decomposable. In our investigation, the condition of purity of modules is crucial. In…
The paper studies a geometrically unfitted finite element method (FEM), known as trace FEM or cut FEM, for the numerical solution of the Stokes system posed on a closed smooth surface. A trace FEM based on standard Taylor-Hood (continuous…
We present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of multigraded modules over the multivariate polynomial ring arising from the hierarchical stabilization…
A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincar\'{e} duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one…
We introduce a new notion of persistence modules endowed with operators. It encapsulates the additional structure on Floer-type persistence modules coming from the intersection product with classes in the ambient (quantum) homology, along…
In this paper, we introduce a family of indecomposable finite-dimensional graded modules for the twisted current algebras. These modules are indexed by an $|R^+|$-tuple of partitions $\bxi=(\xi^{\alpha})_{\alpha\in R^+}$ satisfying a…
This is the first in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global confor- mal invariants"; these are defined to be conformally invariant integrals of geometric scalars.…
Over a family of varieties with singular special fiber, the relative Picard functor (i.e. the moduli space of line bundles) may fail to be compact. We propose a stability condition for line bundles on reducible varieties that is aimed at…
Let $C$ be a smooth irreducible complex projective curve of genus $g \geq 2$ and $M$ the moduli space of stable vector bundles on $C$ of rank $n$ and degree $d$ with $\gcd(n,d)=1$. A generalised Picard sheaf is the direct image on $M$ of…
One-dimensional persistent homology is arguably the most important and heavily used computational tool in topological data analysis. Additional information can be extracted from datasets by studying multi-dimensional persistence modules and…
When filtering a topological space by a single parameter, the theory of quiver representations provides a complete framework for decomposing the resulting persistence module to obtain its barcode. This is achieved by interpreting the…
On a triangulated category $\mathbf D$ equipped with a semiorthogonal decomposition $\mathbf D=\langle{\mathbf D_{1}},{\mathbf D_{2}}\rangle$, Collins and Polishchuk develop a gluing construction of stability condition on $\mathbf D$. The…
In this paper we construct indecomposable vector bundles associated to monads on Cartesian products of odd dimension projective spaces. Specifically we establish the existence of monads on…
As well-known, inner functions play an important role in the study of bounded analytic function theory. In recent years, persistence module theory, as a main tool applied to Topological Data Analysis, has received widespread attention. In…
We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…
We prove a new kind of homological stability theorem for automorphism groups of finitely-generated projective modules over Dedekind domains, which takes into account all possible stabilisation maps between these, rather than only…
Let $k$ be a perfect field of characteristic $p >0$, $U$ be a variety over $k$ and $F$ be a power of Frobenius. We construct the category of overholonomic arithmetical ($F$-)$\D$-modules over $U$ and the category of overholonomic…
We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple…
Recently, bipath persistent homology has been proposed as an extension of standard persistent homology, along with its visualization (bipath persistence diagram) and computational methods. In the setting of standard persistent homology, the…