The Lower Algebraic K-Theory of Virtually Cyclic Subgroups of the Braid Groups of the Sphere and of ZB4(S2)

Language: English

Published by Springer, Palgrave Macmillan Nov 2018, 2018

3319994883 / 9783319994888

Series: Book 119 of 155 - SpringerBriefs in Mathematics

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 92 pp. Englisch.

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Title
The Lower Algebraic K-Theory of Virtually Cyclic Subgroups of the Braid Groups of the Sphere and of ZB4(S2)
Author
John Guaschi
Publisher
Springer, Palgrave Macmillan Nov 2018
Publication year
2018
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3319994883
ISBN 13
9783319994888
Item weight
154 grams
Dimensions
235x155x6 mm
Series
Book 119 of 155: SpringerBriefs in Mathematics

buchversandmimpf2000

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