EAN: 9783319994888

SPRINGERBRIEFS IN MATHEMATICS THE LOWER ALGEB...

This volume deals with the K-theoretical aspects of the group rings of braid groups of the
2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven
strings is computed using a wide variety of tools. Many of the techniques extend to the general
case  and the results reveal new K-theoretical phenomena with respect to the previous study of
other families of groups. The second part of the manuscript focusses on the case of the
4-string braid group of the 2-sphere  which is shown to be hyperbolic in the sense of Gromov.
This permits the computation of the infinite maximal virtually cyclic subgroups of this group
and their conjugacy classes  and applying the fact that this group satisfies the Fibred
Isomorphism Conjecture of Farrell and Jones  leads to an explicit calculation of its lower
K-theory. Researchers and graduate students working in K-theory and surface braid groups will
constitute the primary audience of the manuscript  particularly those interested in the Fibred
Isomorphism Conjecture  and the computation of Nil groups and the lower algebraic K-groups of
group rings. The manuscript will also provide a useful resource to researchers who wish to
learn the techniques needed to calculate lower algebraic K-groups  and the bibliography brings
together a large number of references in this respect.

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