亏格为2的Heegaard分解中的Haken球面(英文)

Haken spheres in Heegaard splittings of genus 2

主要结果描述了透镜空间和圆周与2-球面乘积的亏格为2的Heegaard分解中的两个Haken球面是如何相关的,进而完全解决了亏格为2的Heegaard分解中的Haken球面的相关性问题.

A Haken sphere S in a 3 - manifold M with a Heegaard splitting VOFW is a separating 2 - sphere in M which intersects the Heegaard surface F only in an essential circle in F. It is known that how any two Haken spheres in a genus 2 Heegaard splitting of S3, a connected sum of two lens spaces, a connected sum of a lens space and S^2 × S^1, or S^2 × S^1#S^2 × S^1 are related. In the present paper, we show how any two Haken spheres in a genus 2 Heegaard splitting of a lens space or S： x Sl are related. Thus in all cases of reducible Heegaard splittings of genus 2, the Haken spheres are well understood.