Two-sided, upper and lower, complexity bounds are obtained for a countable family of closed hyperbolic manifolds known as Löbell manifolds. The upper bound is based on the construction of fundamental polyhedra in the Lobachevsky space. The polyhedra are parametrized by an integer parameter n ≥ 5. The lower bound is based on the computation of their volumes and is asymtotic in nature. The upper and lower bounds are linear with respect to n. The Löbell manifolds is obtained by gluing together eight copies of bounded rectangular polyhedron. The vertices are chosen so that the marked vertices are mapped to each other under the identification of the faces.
Two-sided complexity bounds for Löbell manifolds / Vesnin, A. Yu.; Matveev, S. V.; Petronio, C.. - In: DOKLADY MATHEMATICS. - ISSN 1064-5624. - 76:2(2007), pp. 689-691. [10.1134/S1064562407050134]
Two-sided complexity bounds for Löbell manifolds
Petronio C.
2007-01-01
Abstract
Two-sided, upper and lower, complexity bounds are obtained for a countable family of closed hyperbolic manifolds known as Löbell manifolds. The upper bound is based on the construction of fundamental polyhedra in the Lobachevsky space. The polyhedra are parametrized by an integer parameter n ≥ 5. The lower bound is based on the computation of their volumes and is asymtotic in nature. The upper and lower bounds are linear with respect to n. The Löbell manifolds is obtained by gluing together eight copies of bounded rectangular polyhedron. The vertices are chosen so that the marked vertices are mapped to each other under the identification of the faces.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
