A formula on Heegaard genus of self-amalgamated 3-manifolds

Let M be an orientable compact irreducible and ∂-irreducible 3-manifold, and suppose ∂M consists of two boundary components F₁ and F₂ with g(F₁)=g(F₂)>1. Let Mf be the closed orientable 3-manifold obtained by identifying F₁ and F₂ via a homeomorphism f:F₁→F₂. With the assumption that M is small or g(M,F₁)=g(M)+g(F₁), we show that if f is sufficiently complicated, then g(Mf)=g(M,∂M)+1.     

Incompressible surfaces in handlebodies and closed 3-manifolds of Heegaard genus 2

In this paper, we shall prove that for any integer 0$">, 1) a handlebody of genus 2 contains a separating incompressible surface of genus , 2) there exists a closed 3-manifold of Heegaard genus which contains a separating incompressible surface of genus .

     

Twist points of planar domains

We establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains.

     

Computing boundary slopes of 2-bridge links

We describe an algorithm for computing boundary slopes of 2-bridge links. As an example, we work out the slopes of the links obtained by surgery on one component of the Borromean rings. A table of all boundary slopes of all 2-bridge links with 10 or less crossings is also included.

     

Surgery diagrams and open book decompositions of contact 3-manifolds

Summary We show an algorithmic way for finding a compatible open book decomposition on a contact 3-manifold given by contact (±1)-surgery.     

Rudolph diagrams and an analytic realization of the Vitushkin covering

An example of a three-sheeted covering over the ball in ² is constructed. The covering is the union of a four-dimensional ball with an analytic disk. The projection of the ball is a local homeomorphism ramified along the disk, whose projection is a part of an algebraic curve.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 206–224, August, 1996.This research was partially supported by the Russian Foundation for Basic Research under grant No. 93-011-225.     

Edges of Canonical Decompositions for 2-Bridge Knots and Links

Let L=C(a1,..., ak) be a hyperbolic 2-bridge knot or link. We give a family of arcs in S3–L which are ambient isotopic to edges of the canonical decomposition of S3–L if each aj is sufficiently large. This result supports the conjecture that the decomposition of S3–L given by Sakuma–Weeks in [12] is the canonical one.