Reflections on trisection genus
Reflections on trisection genus
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发表时间：
2018-09
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通讯作者：
Michelle Chu;Stephan Tillmann
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作者：
Michelle Chu;Stephan Tillmann
从3流形的代数性质、几何性质和拓扑性质等方面对3流形的Heegaard格及其有限覆盖空间中的Heegaard格的生长进行了广泛的研究。这说明了关于光滑可定向4流形的三分格的类似结果比3流形的对应结果有更一般的答案。在双曲4-流形的情况下，给出了体积的上界和下界，并描述了戴维斯流形的三切分。
The Heegaard genus of a 3-manifold, as well as the growth of Heegaard genus in its finite sheeted cover spaces, has extensively been studied in terms of algebraic, geometric and topological properties of the 3-manifold. This note shows that analogous results concerning the trisection genus of a smooth, orientable 4-manifold have more general answers than their counterparts for 3-manifolds. In the case of hyperbolic 4-manifolds, upper and lower bounds are given in terms of volume and a trisection of the Davis manifold is described.