Toroidal and boundary-reducing Dehn fillings
نویسندگان
چکیده
منابع مشابه
Ja n 19 98 TOROIDAL AND BOUNDARY - REDUCING DEHN FILLINGS
Let M be a simple 3-manifold with a toral boundary component ∂0M . If Dehn filling M along ∂0M one way produces a toroidal manifold and Dehn filling M along ∂0M another way produces a boundary-reducible manifold, then we show that the absolute value of the intersection number on ∂0M of the two filling slopes is at most two. In the special case that the boundary-reducing filling is actually a so...
متن کاملAnnular and Boundary Reducing Dehn Fillings
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...
متن کاملToroidal and Annular Dehn Fillings
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...
متن کاملReducing Dehn filling and toroidal Dehn filling
It is shown that if M is a compact, connected, orientable hyperbolic 3-manifold whose boundary is a torus, and 7‘1, FZ are two slopes on i7M whose associated fillings are respectively a reducible manifold and one containing an essential torus, then the distance between these slopes is bounded above by 4. Under additional hypotheses this bound is improved Consequently the cabling conjecture is s...
متن کاملToroidal Dehn fillings on hyperbolic 3-manifolds
We determine all hyperbolic 3-manifolds M admitting two toroidal Dehn fillings at distance 4 or 5. We show that if M is a hyperbolic 3manifold with a torus boundary component T0, and r, s are two slopes on T0 with ∆(r, s) = 4 or 5 such that M(r) and M(s) both contain an essential torus, then M is either one of 14 specific manifolds Mi, or obtained from M1, M2, M3 or M14 by attaching a solid tor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1999
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(97)00258-7