Boundary slopes and the logarithmic limit set
نویسندگان
چکیده
منابع مشابه
Boundary Slopes and the Logarithmic Limit Set
The A–polynomial of a manifold whose boundary consists of a single torus is generalised to an eigenvalue variety of a manifold whose boundary consists of a finite number of tori, and the set of strongly detected boundary curves is determined by Bergman’s logarithmic limit set, which describes the exponential behaviour of the eigenvalue variety at infinity. This enables one to read off the detec...
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Let rm and rM be the least and greatest finite boundary slopes of a hyperbolic knot K in S . We show that any cyclic surgery slopes of K must lie in the interval (rm − 1/2, rM + 1/2). AMS Classification 57M25; 57M27
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Let X be a norm curve in the SL(2,C)-character variety of a knot exterior M . Let t = ‖β‖/‖α‖ be the ratio of the Culler-Shalen norms of two distinct non-zero classes α, β ∈ H1(∂M,Z). We demonstrate that either X has exactly two associated strict boundary slopes ±t, or else there are strict boundary slopes r1 and r2 with |r1| > t and |r2| < t. As a consequence, we show that there are strict bou...
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We show that for certain hyperbolic manifolds all boundary slopes are slopes of π1-injective immersed surfaces, covered by incompressible embeddings in some finite cover. The manifolds include hyperbolic punctured torus bundles and hyperbolic two-bridge knots.
متن کاملImmersed , Virtually - Embedded , Boundary Slopes
For the figure eight knot, we show that slopes with even numerator are slopes of immersed surfaces covered by incompressible, boundary-incompressible embeddings in some finite cover. 2000 Elsevier Science B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Topology
سال: 2005
ISSN: 0040-9383
DOI: 10.1016/j.top.2004.07.002