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Global Actions, Groupoid Atlases and Applications

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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
http://jhrs.rmi.acnet.ge/volumes/2006/n1a5/