论文信息 - On reducible Heegaard splittings

On reducible Heegaard splittings

Let V∪SW be a reducible Heegaard splitting of genus g = g(S) ⩾ 2. For a maximal prime connected sum decomposition of V ∪SW, let q denote the number of the genus 1 Heegaard splittings of S2 × S1 in the decomposition, and p the number of all other prime factors in the decomposition. The main result of the present paper is to describe the relation of p, q and dim(CV ∩ CW).

[1] R. Daverman,et al. Handbook of Geometric Topology , 2002 .

[2] N. V. Ivanov. On the virtual cohomology dimension of the Teichmüller modular group , 1984 .

[3] William Jaco,et al. Lectures on three-manifold topology , 1980 .

[4] John Hempel,et al. 3-Manifolds as viewed from the curve complex ☆ , 1997, math/9712220.

[5] W. J. Harvey,et al. Boundary Structure of The Modular Group , 1981 .

[6] Martin Scharlemann,et al. Chapter 18 – Heegaard Splittings of Compact 3-Manifolds , 2000, math/0007144.

[7] Nikolai V. Ivanov,et al. Mapping Class Groups , 2001 .

[8] C. McA. Gordon,et al. Reducing heegaard splittings , 1987 .