Knots and Links The Linking Number
7.1 Marking Algorithm
In the first two sections of this chapter, we assume that the input spaces are three-dimensional and torsion-free, as discussed in section 4.2.3. Consequently, we use Z 2 coefficients for computation. Recall from Section 4.3 that using these coefficients greatly simplifies homology: The homology groups are vec- tor spaces, a k-chain is simply the list of simplices with coefficients 1, each simplex is its own inverse, and the group operation is symmetric difference, as shown in Figure 7.1. The only nonzero Betti numbers to be computed are β , β 1 , and β 2 . We also need a filtration ordering of the simplices Definition 2.44. We use 125Parts
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