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Reducing Dehn Fillings and Small Surfaces
Author(s) -
Lee Sangyop,
Oh Seungsang,
Teragaito Masakazu
Publication year - 2006
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1017/s002461150501542x
Subject(s) - klein bottle , mathematics , torus , real projective plane , möbius strip , projective plane , annulus (botany) , pure mathematics , manifold (fluid mechanics) , hyperbolic geometry , plane (geometry) , combinatorics , geometry , projective test , projective space , complex projective space , algebraic geometry , materials science , mechanical engineering , engineering , correlation , composite material
In this paper we investigate the distances between Dehn fillings on a hyperbolic 3‐manifold that yield 3‐manifolds containing essential small surfaces including non‐orientable surfaces. In particular, we study the situations where one filling creates an essential sphere or projective plane, and the other creates an essential sphere, projective plane, annulus, Möbius band, torus or Klein bottle, for all eleven pairs of such non‐hyperbolic manifolds. 2000 Mathematics Subject Classification 57M50.