不可定向4-流形的三切分

Pub Date : 2020-10-14 DOI:10.1307/mmj/20216127

Maggie Miller, Patrick Naylor

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引用次数: 2

摘要

研究光滑紧致非定向4-流形的三等分，并引入具有边界的非定向4-流形的三等分。特别地，我们证明了Laudenbach-Poenaru经典定理的一个非定向类比。因此，存在闭合不可定向4流形的三切图和Kirby图。我们用许多例子讨论了如何将三分理论应用于非定向4流形的设置。

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Trisections of Nonorientable 4-Manifolds

We study trisections of smooth, compact non-orientable 4-manifolds, and introduce trisections of non-orientable 4-manifolds with boundary. In particular, we prove a non-orientable analogue of a classical theorem of Laudenbach-Poenaru. As a consequence, trisection diagrams and Kirby diagrams of closed non-orientable 4-manifolds exist. We discuss how the theory of trisections may be adapted to the setting of non-orientable 4-manifolds with many examples.

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