相关论文: Stratified simplices and intersection homology
This paper is concerned with the primitive cohomology of a smooth projective hypersurface considered as a linear representation for its automorphism group. Using the Lefschetz-Riemann-Roch formula, the character of this representation is…
It is shown that a surjective monotone map $X\to Y$ between finite $T_0$-spaces induces a surjective map on homology. As such a map turns out to be a sequence of edge contractions in the Hasse diagram of $X$, followed by a homeomorphism,…
We study the intersection theory of punctured pseudoholomorphic curves in $4$-dimensional symplectic cobordisms. We first study the local intersection properties of such curves at the punctures. We then use this to develop topological…
A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. In this paper, we study the embedded homology as well as the homology of the (lower-)associated simplicial complexes for hypergraphs. We…
For an arbitrary complex algebraic variety which is not necessarily pure dimensional, the intersection complex can be defined as the direct sum of the Deligne-Goresky-MacPherson intersection complexes of each irreducible component. We give…
In this paper, by refining approximation theorems for holomorphic sections of adjoint line bundles, it is proved that the regular locus of a weakly pseudoconvex complex space admitting a positive line bundle can be holomorphically embedded…
A theorem of Kontsevich relates the homology of certain infinite dimensional Lie algebras to graph homology. We formulate this theorem using the language of reversible operads and mated species. All ideas are explained using a pictorial…
This expository article is an expanded version of talks given at the "Current Developments in Mathematics, 2002" conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the…
Let $X^4$ and $Y^4$ be smooth manifolds and $f: X\to Y$ a branched cover with branching set $B$. Classically, if $B$ is smoothly embedded in $Y$, the signature $\sigma(X)$ can be computed from data about $Y$, $B$ and the local degrees of…
Motivated by connections to intersection homology of toric morphisms, the motivic monodromy conjecture, and a question of Stanley, we study the structure of triangulations of simplices whose local h-polynomial vanishes. As a first step, we…
Within its traditional range of perversity parameters, intersection cohomology is a topological invariant of pseudomanifolds. This is no longer true once one allows superperversities, in which case intersection cohomology may depend on the…
The theory of intersection spaces assigns cell complexes to certain stratified topological pseudomanifolds depending on a perversity function in the sense of intersection homology. The main property of the intersection spaces is Poincar\'e…
Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their…
This paper investigates a novel structure of stratified L-convex groups, defined as groups possessing stratified L-convex structures, in which the group operations are L-convexity-preserving mappings. It is verified that stratified L-convex…
In this article, we introduce a notion of polygraphic homology of a strict $\omega$-category with coefficients in a local system, generalizing the polygraphic homology with coefficients in $\mathbb Z$, introduced by Fran\c{c}ois M\'etayer.…
For a normal surface singularity, the discrepancy between the ordinary and dual middle-perversity intersection complexes over \(\mathbb Z\) is measured by a finite group \(E\). In previous work, \(E\) was identified with link torsion, the…
We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving…
It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group…
A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. By [11], a hypergraph gives an associated simplicial complex. By [4], the embedded homology of a hypergraph is the homology of the infimum chain…
A graph is locally chordal if each of its small-radius balls is chordal. In an earlier work [AKK25], the authors and Kobler proved that locally chordal graphs can be characterized by having chordal local covers, by forbidding short cycles…