Abstract
In this chapter, we compute the homology groups \(H_{n}^{\varGamma }(E_{\mathcal{F}\mathcal{I}\mathcal{N}}(\varGamma ); \mathbb{K}\mathbb{Z}^{-\infty })\), for all 73 split three-dimensional crystallographic groups.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Alves, P. Ontaneda, A formula for the Whitehead group of a three-dimensional crystallographic group. Topology 45(1), 1–25 (2006)
H. Bass, K-theory and stable algebra. Inst. Hautes ’Etudes Sci. Publ. Math. 22, 5–60 (1964)
H. Bass, J. Milnor, J.-P. Serre, Solution of the congruence subgroup problem for SL n (n ≥ 3) and Sp2n (n ≥ 2). Inst. Hautes Études Sci. Publ. Math. 33, 59–137 (1967)
H. Bass, Algebraic K-Theory (W.A. Benjamin, New York, 1968)
D. Carter, Lower K-theory of finite groups. Commun. Algebra 8(20), 1927–1937 (1980)
M. Cohen, A Course in Simple Homotopy Theory (Springer, New York, 1973)
S. Endo, Y. Hironaka, Finite groups with trivial class group. J. Math. Soc. Jpn. 31(1), 161–174 (1979)
J.-F. Lafont, B. Magurn, I.J. Ortiz, Lower algebraic K-theory of certain reflection groups. Math. Proc. Camb. Philos. Soc. 148(2), 193–226 (2010)
J.-F. Lafont, I.J. Ortiz, Lower algebraic K-theory of hyperbolic 3-simplex reflection groups. Comment. Math. Helv. 84, 297–337 (2009)
B. Magurn, Explicit K 1 of some modular groups rings. J. Pure Appl. Algebra 206, 3–20 (2006)
J. Milnor, in Introduction to Algebraic K-Theory. Annals of Mathematics Studies, vol. 72 (Princeton University Press, Princeton) (1971)
R. Oliver, in Whitehead Groups of Finite Groups. London Mathematical Society Lecture Note Series, vol. 132 (Cambridge University Press, Cambridge, 1989)
F. Quinn, Ends of maps II. Invent. Math. 68, 353–424 (1982)
I. Reiner, S. Ullom, Remarks on Class Groups of Integral Group Rings. Symposia Mathematica, vol. XIII (Convegno di Gruppi e loro Rappresentazioni, INDAM, Rome, 1972) (Academic, London, 1974), pp. 501–516
J.-P. Serre, Linear Representations of Finite Groups [translated from the second French edition by Leonard L. Scott]. Graduate Texts in Mathematics, vol. 42 (Springer, New York, 1977)
L.N. Vaserstein, On the stabilization of the general linear group over a ring. Mat. Sb. (N.S.) 79(121), 405–424 (Russian) [translated as Math. USSR-Sb. 8, 383–400 (1969)]
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Farley, D.S., Ortiz, I.J. (2014). The Homology Groups \(H_{n}^{\varGamma }(E_{\mathcal{F}\mathcal{I}\mathcal{N}}(\varGamma ); \mathbb{K}\mathbb{Z}^{-\infty })\) . In: Algebraic K-theory of Crystallographic Groups. Lecture Notes in Mathematics, vol 2113. Springer, Cham. https://doi.org/10.1007/978-3-319-08153-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-08153-3_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08152-6
Online ISBN: 978-3-319-08153-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)