Surface groups in some surgered manifolds

Bart, Anneke

doi:10.1016/s0040-9383(99)00062-2

Cited by 11 publications

(23 citation statements)

References 15 publications

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“…Totally geodesic surfaces can be closed (see [3,4] for instance) or have boundary. Bianchi groups act on hyperbolic space, and the cusps of the orbifold correspond to the number of ideal classes of the ring O d .…”

Section: Background and General Resultsmentioning

confidence: 99%

Immersed and Virtually Embedded Boundary Slopes in Arithmetic Manifolds

Bart¹

2004

J. Knot Theory Ramifications

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Section: Background and General Resultsmentioning

confidence: 99%

Immersed and Virtually Embedded Boundary Slopes in Arithmetic Manifolds

Bart¹

2004

J. Knot Theory Ramifications

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“…Furthermore, we may adjust φ and φ ′ so that r intersects r ′ in a single point, v . Let 1]. But this path δ must necessarily pass through π −1 (v), and so there is some…”

Section: Lemma 214 Suppose That [φ]mentioning

confidence: 99%

“…In [1], Bart shows that M contains a closed, immersed, totally geodesic surface Σ which remains π 1 -injective after all but at most thirteen fillings. The main tool used in Bart's proof is the Gromov-Thurston 2π Theorem, in which an explicit negatively curved metric is constructed on the filled manifold [4].…”

Section: Examplesmentioning

confidence: 99%

Geometry of pseudocharacters

Manning

2005

Geom. Topol.

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If G is a group, a pseudocharacter f: G-->R is a function which is "almost" a homomorphism. If G admits a nontrivial pseudocharacter f, we define the space of ends of G relative to f and show that if the space of ends is complicated enough, then G contains a nonabelian free group. We also construct a quasi-action by G on a tree whose space of ends contains the space of ends of G relative to f. This construction gives rise to examples of "exotic" quasi-actions on trees.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper26.abs.htm

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“…On the other hand, if F is closed, totally geodesic and has a bounded genus, then the depth of F in N is bounded above by a constant which is independent of N and M . See for example Bart [2].…”

Section: Introductionmentioning

confidence: 99%

Depth of pleated surfaces in toroidal cusps of hyperbolic 3–manifolds

2009

Algebr. Geom. Topol.

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Let F be a closed essential surface in a hyperbolic 3-manifold M with a toroidal cusp N . The depth of F in N is the maximal distance from points of F in N to the boundary of N . It will be shown that if F is an essential pleated surface which is not coannular to the boundary torus of N then the depth of F in N is bounded above by a constant depending only on the genus of F . The result is used to show that an immersed closed essential surface in M which is not coannular to the torus boundary components of M will remain essential in the Dehn filling manifold M (γ) after excluding Cg curves from each torus boundary component of M , where Cg is a constant depending only on the genus g of the surface.

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Surface groups in some surgered manifolds

Cited by 11 publications

References 15 publications

Immersed and Virtually Embedded Boundary Slopes in Arithmetic Manifolds

Immersed and Virtually Embedded Boundary Slopes in Arithmetic Manifolds

Geometry of pseudocharacters

Depth of pleated surfaces in toroidal cusps of hyperbolic 3–manifolds

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