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2 results on '"Rui Feng Qiu"'

1. 3–Manifold Containing Separating Incompressible Surfaces of All Positive Genera

Author

Rui Feng Qiu and Ji Ming Ma

Subjects
Combinatorics, Applied Mathematics, General Mathematics, Mathematical analysis, Compressibility, Incompressible surface, 3-manifold, Knot (mathematics), Mathematics
Abstract

In this paper, we shall prove that for any orientable 3–manifold M, there is a link L = K ∪ K1 ∪ K2 ∪ K3 with four components in M, such that the complement of L, say ML, contains separating essential closed surfaces of all positive genera.

Published
2005

2. Boundary reducible handle additions on simple 3-manifolds

Author

Rui Feng Qiu, Yannan Li, and Mingxing Zhang

Subjects
Applied Mathematics, General Mathematics, Astrophysics::High Energy Astrophysical Phenomena, Boundary (topology), Geometric Topology (math.GT), Mathematics::Geometric Topology, Manifold, 57M50, Combinatorics, Mathematics - Geometric Topology, Simple (abstract algebra), Genus (mathematics), FOS: Mathematics, Component (group theory), Mathematics
Abstract

Let $M$ be a simple manifold, and $F$ be a component of $\partial M$ of genus two. For a slope $\gamma$ on $F$, we denote by $M(\gamma)$ the manifold obtained by attaching a 2-handle to $M$ along a regular neighborhood of $\gamma$ on $F$. In this paper, we shall prove that there is at most one separating slope $\gamma$ on $F$ so that $M(\gamma)$ is $\partial$-reducible., Comment: 16 pages, 20 figures

Published
2007

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