On complexity of three-dimensional hyperbolic manifolds with geodesic boundary

The nonintersecting classes ℋp,q are defined, with p, q ∈ ℕ and p ≥ q ≥ 1, of orientable hyperbolic 3-manifolds with geodesic boundary. If M ∈ ℋp,q, then the complexity c(M) and the Euler characteristic χ(M) of M are related by the formula c(M) = p−χ(M). The classes ℋq,q, q ≥ 1, and ℋ2,1 are known to contain infinite series of manifolds for each of which the exact values of complexity were found. There is given an infinite series of manifolds from ℋ3,1 and obtained exact values of complexity for these manifolds. The method of proof is based on calculating the ɛ-invariants of manifolds.