Algebraic transversality is the chain complex analogue of the geometric transversality technique used to construct fundamental domains for infinite cyclic covers of compact manifolds and finite CW complexes. Refer to Ranicki [244, Chap. 4] for a previous account of algebraic transversality: here, only the additional results required for the new applications are proved. The construction in Part Two of the algebraic invariants of knots will make use of the L-theory version of algebraic transversality for chain complexes with Poincaré duality, the analogue of the geometric transversality construction of a Seifert surface fundamental domain for the infinite cyclic cover of a knot complement.
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