Hyperbolic knot complements without closed embedded totally geodesic surfaces

Authors
Ichihara, K Ozawa, M
Citation
K. Ichihara et M. Ozawa, Hyperbolic knot complements without closed embedded totally geodesic surfaces, J AUS MAT A, 68, 2000, pp. 379-386
Citations number
10
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
ISSN journal
02636115 → ACNP
Volume
68
Year of publication
2000
Part
3
Pages
379 - 386
Database
ISI
SICI code
0263-6115(200006)68:<379:HKCWCE>2.0.ZU;2-#
Abstract
It is conjectured that a hyperbolic knot complement does not contain a clos ed embedded totally geodesic surface. In this paper, we show that there are no such surfaces in the complements of hyperbolic S-bridge knots and doubl e torus knots. Some topological criteria for a closed essential surface fai ling to be totally geodesic are given. Roughly speaking, sufficiently 'comp licated' surfaces cannot be totally geodesic. 2000 Mathematics subject clas sification: primary 57M25, 57M50.