Homotopy Motions of Surfaces in 3-Manifolds

Strong Homotopy Equivalence of 3-manifolds

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...

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 .

Deformation of Homotopy into Isotopy in Oriented 3-manifolds

We will show that deformation quantization in skein theory of oriented 3-manifolds is induced from a topological deformation quantization of the fundamental 2-groupoid of the space of immersions of circles in M . The structure of skein module and its relations with string topology homomorphisms appear through representations of the groupoid structure into the set the objects. The deformation of...

Minimal 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 ...