Titlebook: Algebraic K-theory of Crystallographic Groups; The Three-Dimensiona Daniel Scott Farley,Ivonne Johanna Ortiz Book 2014 Springer Internation

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Arithmetic Classification of Pairs (,, ,),Let . be a lattice in ., and let . ≤ .(3) be a point group such that . ? . = .. In this chapter, we classify pairs (., .) up to arithmetic equivalence (defined below). The equivalence classes of pairs (., .) are in one-to-one correspondence with isomorphism classes of split crystallographic groups (see Chap.?4).

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The Split Three-Dimensional Crystallographic Groups,An . is a discrete, cocompact subgroup of the group of isometries of Euclidean .-space. Each . ∈ . can be written in the form .. + .., where .. ∈ .. is a translation and .. ∈ .(.).

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A Splitting Formula for Lower Algebraic,-Theory,Let . be a three-dimensional crystallographic group with lattice . and point group .. (We do not assume that . is a split crystallographic group.) In this chapter, we describe a simple construction of . and derive a splitting formula for the lower algebraic .-theory of any three-dimensional crystallographic group.

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The Homology Groups ,,In this chapter, we compute the homology groups ., for all 73 split three-dimensional crystallographic groups.

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