Vertical 3-manifolds in simplified (2, 0)-trisections of 4-manifolds

Nobutaka Asano

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arXiv · 2010.08239

Vertical 3-manifolds in simplified (2, 0)-trisections of 4-manifolds

Nobutaka Asano

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Abstract

We classify the $3$-manifolds obtained as the preimages of arcs on the plane for simplified $(2, 0)$-trisection maps, which we call vertical $3$-manifolds. Such a $3$-manifold is a connected sum of a $6$-tuple of vertical $3$-manifolds over specific $6$ arcs. Consequently, we show that each of the $6$-tuples determines the source $4$-manifold uniquely up to orientation reversing diffeomorphisms. We also show that, in contrast to the fact that summands of vertical $3$-manifolds of simplified $(2, 0)$-trisection maps are lens spaces, there exist infinitely many simplified $(2, 0)$-$4$-section maps that admit hyperbolic vertical $3$-manifolds.

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BibTeX RIS

Nobutaka Asano. 2020-10-16. Vertical 3-manifolds in simplified (2, 0)-trisections of 4-manifolds. https://arxiv.org/abs/2010.08239

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