Abstract
We can now compute the lower algebraic K-theory of the 73 split crystallographic groups. Recall that Theorem 5.1 tells us that, for all such groups Γ, we have an isomorphism
For all 73 of our groups, we have:
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Explicitly computed in Chap. 7 the homology groups
$$\displaystyle{H_{{\ast}}^{\varGamma }(E_{ \mathcal{F}\mathcal{I}\mathcal{N}}(\varGamma ); \mathbb{K}\mathbb{Z}^{-\infty }),}$$and summarized the results in Table 7.8.
Keywords
- Group Theory
- Point Group
- Explicit Calculation
- Homology Group
- Cell Complex
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F.T. Farrell, L. Jones, The lower algebraic K-theory of virtually infinite cyclic groups. K Theory 9, 13–30 (1995)
C. Weibel, NK 0 and NK 1 of the groups C 4 and D 4. Comment. Math. Helv. 84, 339–349 (2009)
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Farley, D.S., Ortiz, I.J. (2014). Summary. 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_10
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DOI: https://doi.org/10.1007/978-3-319-08153-3_10
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