Maximal triads and prime decompositions of surfaces embedded in $3$-manifolds
نویسندگان
چکیده
منابع مشابه
Separability 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 کاملCanonical Decompositions of 3–Manifolds
We describe a new approach to the canonical decompositions of 3–manifolds along tori and annuli due to Jaco–Shalen and Johannson (with ideas from Waldhausen) — the so-called JSJ–decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus–torus theorems, and the theory of Seifert fibrations does not need to be developed i...
متن کاملMinimal surfaces and particles in 3-manifolds
We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic, anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these manifolds admit “nice” foliations and explicit metrics, and whether the space of these metrics has a simple description in terms of Teichmüller theory. In the hyperbolic settings both questions have positive answers for a certain subset of the quasi-...
متن کاملMaximal symmetry groups of hyperbolic 3-manifolds
Every finite group acts as the full isometry group of some compact hyperbolic 3-manifold. In this paper we study those finite groups which act maximally, that is when the ratio |Isom(M)|/vol(M) is maximal among all such manifolds. In two dimensions maximal symmetry groups are called Hurwitz groups, and arise as quotients of the (2,3,7)–triangle group. Here we study quotients of the minimal co-v...
متن کاملIncompressibility 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 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: Transactions of the American Mathematical Society
سال: 1992
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1992-1062195-9