Hyperbolic knot complements without closed embedded totally geodesic surfaces
2000 ◽
Vol 68
(3)
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pp. 379-386
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Keyword(s):
AbstractIt is conjectured that a hyperbolic knot complement does not contain a closed embedded totally geodesic surface. In this paper, we show that there are no such surfaces in the complements of hyperbolic 3-bridge knots and double torus knots. Some topological criteria for a closed essential surface failing to be totally geodesic are given. Roughly speaking, sufficiently ‘complicated’ surfaces cannot be totally geodesic.
1991 ◽
Vol 34
(1)
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pp. 77-88
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Keyword(s):
2006 ◽
Vol 6
(3)
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pp. 1413-1428
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1994 ◽
Vol 116
(2)
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pp. 339-351
Keyword(s):
2006 ◽
Vol 58
(4)
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pp. 673-690
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Keyword(s):
2002 ◽
Vol 118
(3)
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pp. 309-328
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2005 ◽
Vol 133
(12)
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pp. 3735-3744
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2013 ◽
Vol 22
(13)
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pp. 1350072
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