三维流形中的交替Heegaard图和Williams螺线管吸引子
Alternating Heegaard diagrams and Williams solenoid attractors in 3--manifolds
摘要：
在亏格为2的可定向闭曲面上，我们找到了所有具有“交错”或“弱交错”性质的Heegaard图。利用这些图，我们给出了无穷多个亏格的两个3-流形，每个流形都有一个自同构，其非奇异集由两个Williams流形，一个吸引子和一个排斥子组成。这些流形包含一半的棱镜流形，庞加莱的同调3-球和许多其他塞弗特流形，所有整数Dehn手术的数字8结，也有许多连接和。结果表明，许多3-流形都存在一种具有一定稳定性的“平移”。
英文摘要：
We find all Heegaard diagrams with the property "alternating" or "weakly alternating" on a genus two orientable closed surface. Using these diagrams we give infinitely many genus two 3--manifolds, each admits an automorphism whose non-wondering set consists of two Williams solenoids, one attractor and one repeller. These manifolds contain half of Prism manifolds, Poincaré's homology 3--sphere and many other Seifert manifolds, all integer Dehn surgeries on the figure eight knot, also many connected sums. The result shows that many kinds of 3--manifolds admit a kind of "translation" with certain stability.
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