03202nam a22005295i 4500 978-3-319-08153-3 DE-He213 20210702074844.0 cr nn 008mamaa 140827s2014 gw | s |||| 0|eng d 9783319081533 978-3-319-08153-3 10.1007/978-3-319-08153-3 doi QA612.33 PBPD bicssc MAT002010 bisacsh PBPD thema 512.66 23 Farley, Daniel Scott. author. aut http://id.loc.gov/vocabulary/relators/aut Algebraic K-theory of Crystallographic Groups [electronic resource] : The Three-Dimensional Splitting Case / by Daniel Scott Farley, Ivonne Johanna Ortiz. 1st ed. 2014. Cham : Springer International Publishing : Imprint: Springer, 2014. X, 148 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Mathematics, 0075-8434 ; 2113 The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory. In cases where the conjecture is known to be a theorem, it gives a powerful method for computing the lower algebraic K-theory of a group. This book contains a computation of the lower algebraic K-theory of the split three-dimensional crystallographic groups, a geometrically important class of three-dimensional crystallographic group, representing a third of the total number. The book leads the reader through all aspects of the calculation. The first chapters describe the split crystallographic groups and their classifying spaces. Later chapters assemble the techniques that are needed to apply the isomorphism theorem. The result is a useful starting point for researchers who are interested in the computational side of the Farrell-Jones isomorphism conjecture, and a contribution to the growing literature in the field. K-theory. Group theory. Manifolds (Mathematics). Complex manifolds. K-Theory. https://scigraph.springernature.com/ontologies/product-market-codes/M11086 Group Theory and Generalizations. https://scigraph.springernature.com/ontologies/product-market-codes/M11078 Manifolds and Cell Complexes (incl. Diff.Topology). https://scigraph.springernature.com/ontologies/product-market-codes/M28027 Ortiz, Ivonne Johanna. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) Springer Nature eBook Printed edition: 9783319081540 Printed edition: 9783319081526 Lecture Notes in Mathematics, 0075-8434 ; 2113 https://doi.org/10.1007/978-3-319-08153-3 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM Mathematics and Statistics (SpringerNature-11649) Mathematics and Statistics (R0) (SpringerNature-43713)