Cremona maps of de Jonqui\`eres type

This paper is concerned with suitable generalizations of a plane de Jonqui`eres map to higher dimensional space ${\mathbb{P}}^n$ with $n\ge 3$. For each given point of ${\mathbb{P}}^n$ there is a subgroup of the entire Cremona group of dimension $n$ consisting of such maps. One studies both geometric and group-theoretical properties of this notion. In the case where $n=3$ one describes an explicit set of generators of the group and gives a homological characterization of a basic subgroup thereof.