亏格为2的Heegaard分解中的Haken球面(英文)  

Haken spheres in Heegaard splittings of genus 2

作　　者：雷逢春[1] 李阳[1] 

机构地区：[1]哈尔滨工业大学数学系,黑龙江哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2006年第5期603-608,共6页Journal of Natural Science of Heilongjiang University

基　　金：Supported by Natural Science Foundation of China (10571034); AGrant of the Outstanding Youth Fellowship of Heilongjiang Province

摘　　要：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.

关 键 词：3-流形 HEEGAARD分解 Haken球面 

分 类 号：O189.1[理学—数学]