A new approach to van Kampen lemma
Carmelo Vaccaro · arXiv (Cornell University) · 2008
Given a group presentation, we show that its relators can be obtained as outputs of a certain family of algorithms. We introduce an application going from the set of these algorithms to the natural numbers and we show that the area of a relator (and therefore the Dehn function of the presentation) can be defined by means of this application. This permits to simplify the definition of hyperbolic groups. The paper presents also a new approach to van Kampen lemma, of which it gives a formal proof. Key words and phrases: reduced form of a relator, van Kampen lemma, straight line programs, recursively defined sets, area of a relator,