Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций
Конференция: Groups and Graphs, Metrics and Manifolds; Yekaterinburg; Yekaterinburg
Год издания: 2017
Аннотация: A Euclidean structure on the figure-eight knot 41 arises when its conical angle a equals 2n; this is due to Thurston [1]. An explicit construction of fundamental set for a cone-manifold 4i (a) in E3 was given in [2]. The existence of the euclidean structure on figure-eight with a bridge was shown in [3]. In the present work we consПоказать полностьюider a two-parameter family of cone manifolds 41 (a, 7) which singular set is the figure-eight knot with a bridge with conical angles a and 7 along them. For such cone manifolds we construct a fundamental set. That is a non-convex polyhedron P having 22 triangular faces and 12 vertices embedded into the Cayley-Klein model of ff3. We establish existence conditions for the hyperbolic structure on 41(a, 7). The domain of existence of such manifolds is bordered by following curves (1) (2) (3) 5 Y2(1 -2 Y2(1 - 10 Y2 (1 X )2 + YX (4 X - 5) + X (3 - X) + Y = 1, X ) + 2 X = 1, -X ) + 2 Y (1 - 4 X ) = 5, where X = cos a, Y = cos 0 and 0 is the angle between two opposite edges of P forming the knot 41 as the component of the singular set. 41 ( a, 7) results of [3]. The curve (3) corresponds to the case 7 = 2n when the bridge disappears as the component of 41 ( a)
Журнал: Groups and Graphs, Metrics and Manifolds
Номера страниц: 34-34
Издатель: Уральский федеральный университет имени первого Президента России Б.Н. Ельцина