TY - JOUR

T1 - On complexity of three-dimensional hyperbolic manifolds with geodesic boundary

AU - Vesnin, A. Yu

AU - Fominykh, E. A.

PY - 2012/7/1

Y1 - 2012/7/1

N2 - The nonintersecting classes ℋ p,q are defined, with p, q ∈ ℕ and p ≥ q ≥ 1, of orientable hyperbolic 3-manifolds with geodesic boundary. If M ∈ ℋ p,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 ℋ q,q, q ≥ 1, and ℋ 2,1 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 ℋ 3,1 and obtained exact values of complexity for these manifolds. The method of proof is based on calculating the e{open}-invariants of manifolds.

AB - The nonintersecting classes ℋ p,q are defined, with p, q ∈ ℕ and p ≥ q ≥ 1, of orientable hyperbolic 3-manifolds with geodesic boundary. If M ∈ ℋ p,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 ℋ q,q, q ≥ 1, and ℋ 2,1 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 ℋ 3,1 and obtained exact values of complexity for these manifolds. The method of proof is based on calculating the e{open}-invariants of manifolds.

KW - complexity of manifolds

KW - hyperbolic manifolds

UR - http://www.scopus.com/inward/record.url?scp=84865462828&partnerID=8YFLogxK

U2 - 10.1134/S0037446612040052

DO - 10.1134/S0037446612040052

M3 - Article

AN - SCOPUS:84865462828

VL - 53

SP - 625

EP - 634

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -