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

arXiv2010.08239MaRDI QIDQ6351470

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Publication date: 16 October 2020

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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