EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 6 June 2010. For the current production of this journal, please refer to http://www.springer.com/mathematics/geometry/journal/40062.

Global Actions, Groupoid Atlases and Applications

Global Actions, Groupoid Atlases and Applications

A. Bak, R. Brown, G. Minian and T. Porter

Global actions were introduced by A. Bak to give a combinatorial approach to higher $K$-theory, in which control is kept of the elementary operations through paths and paths of paths. This paper is intended as an introduction to this circle of ideas, including the homotopy theory of global actions, which one obtains naturally from the notion of path of elementary operations. Emphasis is placed on developing examples taken from combinatorial group theory, as well as $K$-theory. The concept of groupoid atlas plays a clarifying role.

Journal of Homotopy and Related Structures, Vol. 1(2006), No. 1, pp. 101-167