A groupoid should be thought of as a group with many objects, or with many identities. A
precise definition is given below. A groupoid with one object is essentially just a group. So …

Topology and Groupoids Page 1 TOPOLOGY AND GROUPOIDS: A Geometric Account of
General Topology, Homotopy Types and the Fundamental Groupoid Ronald Brown, BA, MA …

This talk gave a sketch of the contents and background to a book with the titleNonabelian
algebraic topology'being written under support of a Leverhulme Emeritus Fellowship (2002 …

This set of notes, for graduate students who are specializing in algebraic topology, adopts a
novel approach to the teaching of the subject. It begins with a survey of the most beneficial …

Motivated by constructions in topological data analysis and algebraic combinatorics, we
study homotopy theory on the category of Čech closure spaces Cl, the category whose …

The amenable category is a variant of the Lusternik–Schnirelman category, based on covers
by amenable open subsets. We study the monotonicity problem for degree-one maps and …

These expository notes are dedicated to the study of the topology of configuration spaces of
manifolds. We give detailed computations of many invariants, including the fundamental …

We give a general version of theorems due to Seifert–van Kampen and Brown about the
fundamental group of topological spaces. We consider here the fundamental group of a …

Abstract A Seifert–Van Kampen theorem describes the fundamental group of a space in
terms of the fundamental groups of the constituents of a covering and the configuration of …

The aim of this article is to explain a philosophy for applying the 1-dimensional and higher
dimensional Seifert–van Kampen Theorems, and how the use of groupoids and strict higher …