Related papers: Equivalence Between Four Models of Associahedra

We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.

In this article, we investigate the cobordism maps on periodic Floer homology (PFH). In the first part of the paper, we define the cobordism maps on PFH via Seiberg Witten theory as well as the isomorphism between PFH and Seiberg Witten…

We propose a classification of polyhedra (planar, $3$-connected graphs) according to their type i.e., their set of quantities of common neighbours for each pair of distinct vertices. For every (finite) set of non-negative integers, we…

Steenrod homotopy theory is a framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; from another viewpoint, it studies the topology of the lim^1 functor (for inverse sequences of groups). This…

We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a…

We describe some metric properties of incomparability graphs. We consider the problem of the existence of infinite paths, either induced or isometric, in the incomparability graph of a poset. Among other things, we show that if the…

Given a connected graph G with p vertices and q edges, the G-graphicahedron is a vertex-transitive simple abstract polytope of rank q whose edge-graph is isomorphic to a Cayley graph of the symmetric group S_p associated with G. The paper…

We use the concept of a Kirchhoff resistor network (alternatively random walk on a network) to probe connected graphs and produce symmetry revealing canonical labelings of the graph(s) nodes and edges.

Let $f:X-->Y$ be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups $f^*:IH^*(Y)-->IH^*(X)$ compatible with the induced homomorphism on…

Let X be the locally symmetric space associated to a reductive $\mathbb Q$-group G and an arithmetic subgroup $\Gamma$. An L-module M is a combinatorial model of a constructible complex of sheaves on $\widehat X$, the reductive Borel-Serre…

For any $r\geq 1$ and $\mathbf{n} \in \mathbb{Z}_{\geq0}^r \setminus \{\mathbf0\}$ we construct a poset $W_{\mathbf{n}}$ called a 2-associahedron. The 2-associahedra arose in symplectic geometry, where they are expected to control maps…

This article approaches the counting of subgraphs, in terms of signature-type functionals defined over combinatorial Hopf algebras of graphs. Well-known algebraic identities that arise in the context of counting subgraphs are then captured…

We give a simple description of the face poset of the biassociahedra that generalizes, in a straightforward manner, the description of the faces of the Stasheff's associahedra via planar trees.

A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph's end-structure. Using a combinatorial theorem of…

In this article we use the combinatorial and geometric structure of manifolds with embedded cylinders in order to develop an adiabatic decomposition of the Hodge cohomology of these manifolds. We will on the one hand describe the adiabatic…

We exhibit isomorphisms of Grassmann spaces and their relationship with collineations and embeddings of the underlying projective spaces.

We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if K is a shifted simplicial complex on n vertices, X_1,..., X_n are spaces and CX_i is the cone on X_i, then the polyhedral product determined by K and the pairs (CX_i,X_i) is…

A "biased expansion" of a graph is a kind of branched covering graph with additional structure related to combinatorial homotopy of circles. Some but not all biased expansions are constructed from groups ("group expansions"); these include…

Bisztriczky defines a multiplex as a generalization of a simplex, and an ordinary polytope as a generalization of a cyclic polytope. This paper presents results concerning the combinatorics of multiplexes and ordinary polytopes. The flag…

The integrability problem for transitive Lie algebroids can be looked at from different perspectives, revealing an interplay between cohomological methods and homotopical constructions. Mackenzie introduced a cohomological obstruction…