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Fundamental Domains for Actions on Spaces of Planes

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2113)

Abstract

Theorem 5.1 showed that the lower algebraic K-theory of any crystallographic group can be computed in two pieces. In Chap. 7, we completed the first half of the computation for the 73 split three-dimensional crystallographic groups. The results obtained are summarized in Table 7.8.

Keywords

  • Vertical Axis
  • Group Theory
  • Homology Group
  • Cell Complex
  • Fundamental Domain

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References

  1. D.R. Harmon, NK 1 of finite groups. Proc. Am. Math. Soc. 100, 229–232 (1987)

    MATH  MathSciNet  Google Scholar 

  2. D. Juan-Pineda, R. Ramos, On the vanishing of twisted nil groups. J. K Theory 3(1), 153–163 (2009)

    CrossRef  MATH  MathSciNet  Google Scholar 

  3. J.-F. Lafont, I.J. Ortiz, Relating the Farrell Nil-groups to the Waldhausen Nil-groups. Forum Math. 20, 445–455 (2008)

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© 2014 Springer International Publishing Switzerland

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Farley, D.S., Ortiz, I.J. (2014). Fundamental Domains for Actions on Spaces of Planes. 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_8

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