0. Introduction A number of questions from a variety of areas of mathematics lead one to the
problem of analyzing the topology of as implicial complex. We will see some examples in …

These lecture notes for the IAS/Park City Graduate Summer School in Geometric
Combinatorics (July 2004) provide an overview of poset topology. These notes include …

This book is a revised version of my 2005 thesis [71] for the degree of Doctor of Philosophy
at the Royal Institute of Technology (KTH) in Stockholm. The whole idea of writing a …

We recall that the calculation of homology with integer coefficients of a simplicial complex
reduces to the calculation of the Smith Normal Form of the boundary matrices which in …

A variety of questions in combinatorics lead one to the task of analyzing the topology of a
simplicial complex, or a more general cell complex. However, there are few general …

Complexes of (not) connected graphs, hypergraphs and their homology appear in the
construction of knot invariants given by Vassiliev [38, 39, 41]. In this paper we study the …

This paper is a glossary of notions and methods related to the topological theory of affine
plane arrangements, including braid groups, configuration spaces, order complexes …

Discrete Morse theory for complexes of 2-connected graphs - ScienceDirect Skip to main
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We propose a new method of computing cohomology groups of spaces of knots in $\R^ n $,
$ n\ge 3$, based on the topology of configuration spaces and two-connected graphs, and …

Using techniques from Robin Forman's discrete Morse theory, we obtain information about
the homology and homotopy type of some graph complexes. Specifically, we prove that the …