Dehn fillings and elementary splittings
نویسندگان
چکیده
منابع مشابه
Dehn Fillings and Elementary Splittings
We consider conditions on relatively hyperbolic groups about the non-existence of certain kinds of splittings, and show these properties persist in long Dehn fillings. We deduce that certain connectivity properties of the Bowditch boundary persist un-
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Suppose M is a hyperbolic 3-manifold which admits two Dehn fillings M(r1) and M(r2) such that M(r1) contains an essential torus and M(r2) contains an essential annulus. It is known that ∆ = ∆(r1, r2) ≤ 5. We will show that if ∆ = 5 then M is the Whitehead sister link exterior, and if ∆ = 4 then M is the exterior of either the Whitehead link or the 2-bridge link associated to the rational number...
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Surfaces of non-negative Euler characteristic, i.e., spheres, disks, tori and annuli, play a special role in the theory of 3-dimensional manifolds. For example, it is well known that every (compact, orientable) 3-manifold can be decomposed into canonical pieces by cutting it along essential surfaces of this kind [K], [M], [Bo], [JS], [Jo1]. Also, if (as in [Wu3]) we call a 3-manifold that conta...
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We prove an explicit, quantitative criterion that ensures the Heegaard surfaces in Dehn fillings behave “as expected.” Given a cusped hyperbolic 3-manifold X, and a Dehn filling whose meridian and longitude curves are longer than 2π(2g − 1), we show that every genus g Heegaard splitting of the filled manifold is isotopic to a splitting of the original manifold X. The analogous statement holds f...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2018
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7017