Department of Mathematics, University of California, Davis, CA 95616.
Department of Mathematics, University of Georgia, Athens, GA 30602.
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10861-10868. doi: 10.1073/pnas.1717170115. Epub 2018 Oct 22.
Given a handle decomposition of a 4-manifold with boundary and an open book decomposition of the boundary, we show how to produce a trisection diagram of a trisection of the 4-manifold inducing the given open book. We do this by making the original proof of the existence of relative trisections more explicit in terms of handles. Furthermore, we extend this existence result to the case of 4-manifolds with multiple boundary components and show how trisected 4-manifolds with multiple boundary components glue together.
给定一个带边界的 4 维流形的把手分解和边界的开贝叶斯分解，我们展示如何生成 4 维流形的三分叉的三分叉图，从而诱导给定的开贝叶斯。我们通过使相对三分叉存在的原始证明在手柄方面更加明确来做到这一点。此外，我们将此存在结果扩展到具有多个边界分量的 4 维流形的情况，并展示如何将具有多个边界分量的三分叉 4 维流形粘在一起。
