Reflections on trisection genus

Michelle Chu; Stephan Tillmann

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arXiv · 1809.04801

Reflections on trisection genus

Michelle Chu·Stephan Tillmann

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Abstract

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.

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Michelle Chu, Stephan Tillmann. 2018-09-13. Reflections on trisection genus. https://arxiv.org/abs/1809.04801

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