Handle additions producing essential surfaces
نویسندگان
چکیده
منابع مشابه
Reducible and ∂-reducible Handle Additions
Let M be a simple 3-manifold with F a component of ∂M of genus at least two. For a slope α on F , we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F . Suppose that α and β are two separating slopes on F such that M(α) and M(β) are reducible. Then the distance between α and β is at most 2. As a corollary, if g(F ) = 2, then there is at mos...
متن کاملHyperbolic Manifolds and Degenerating Handle Additions
A 2-handle addition on the boundary of a hyperbolic 3-manifold M is called degenerating if the resulting manifold is not hyperbolic. There are examples that some manifolds admit infinitely many degenerating handle additions. But most of them are not “basic”. (See section 1 for definitions.) Our first main theorem shows that there are only finitely many basic degenerating handle additions. We al...
متن کاملBoundary reducible handle additions on simple 3 - manifolds
Let M be a simple manifold, and F be a component of ∂M of genus two. For a slope γ on F , we denote by M(γ) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of γ on F . In this paper, we shall prove that there is at most one separating slope γ on F so that M(γ) is ∂-reducible.
متن کاملComparing 2-handle Additions to a Genus 2 Boundary Component
A theorem concerning the effects of attaching a 2–handle to a suture on the boundary of a sutured manifold is used to compare the effects of two 2-handle attachments to a genus 2 boundary component of a compact, orientable 3–manifold. We obtain a collection of results relating the euler characteristic of a surface in one of the resulting 3– manifolds to the intersection number of the two curves...
متن کاملHandle Addition for Doubly-periodic Scherk Surfaces
We prove the existence of a family of embedded doubly periodic minimal surfaces of (quotient) genus g with orthogonal ends that generalizes the classical doubly periodic surface of Scherk and the genus-one Scherk surface of Karcher. The proof of the family of immersed surfaces is by induction on genus, while the proof of embeddedness is by the conjugate Plateau method.
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: Pacific Journal of Mathematics
سال: 2007
ISSN: 0030-8730
DOI: 10.2140/pjm.2007.229.233