Incompressibility of surfaces in surgered 3-manifolds
نویسندگان
چکیده
منابع مشابه
Incompressibility of Surfaces in Surgered 3-Manifolds
The problem we consider in this paper was raised in [3]. Suppose T is a torus on the boundary of an orientable 3-manifold X, and S is a surface on ∂X − T which is incompressible in X. A slope γ is the isotopy class of a nontrivial simple closed curve on T . Denote by X(γ) the manifold obtained by attaching a solid torus to X so that γ is the slope of the boundary of a meridian disc. Given two s...
متن کاملSeparability of embedded surfaces in 3-manifolds
We prove that if S is a properly embedded π1-injective surface in a compact 3-manifold M , then π1S is separable in π1M .
متن کاملIncompressibility and Least-area Surfaces
We show that if F is a smooth, closed, orientable surface embedded in a closed, orientable 3-manifold M such that for each Riemannian metric g on M , F is isotopic to a least-area surface F (g), then F is incompressible.
متن کاملMinimal Surfaces in Geometric 3-manifolds
In these notes, we study the existence and topology of closed minimal surfaces in 3-manifolds with geometric structures. In some cases, it is convenient to consider wider classes of metrics, as similar results hold for such classes. Also we briefly diverge to consider embedded minimal 3-manifolds in 4-manifolds with positive Ricci curvature, extending an argument of Lawson to this case. In the ...
متن کاملEssential Closed Surfaces in Bounded 3-manifolds
A question dating back to Waldhausen [10] and discussed in various contexts by Thurston (see [9]) is the problem of the extent to which irreducible 3-manifolds with infinite fundamental group must contain surface groups. To state our results precisely, it is convenient to make the definition that a map i : S # M of a closed, orientable connected surface S is essential if it is injective at the ...
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
سال: 1992
ISSN: 0040-9383
DOI: 10.1016/0040-9383(92)90020-i