Mathematical Research Letters

Volume 25 (2018)

Number 5

Trisections and spun four-manifolds

Pages: 1497 – 1524



Jeffrey Meier (Department of Mathematics, University of Georgia, Athens, Ga., U.S.A.)


We study trisections of $4$-manifolds obtained by spinning and twist-spinning $3$-manifolds, and we show that, given a (suitable) Heegaard diagram for the $3$-manifold, one can perform simple local modifications to obtain a trisection diagram for the $4$-manifold. We also show that this local modification can be used to convert a (suitable) doubly-pointed Heegaard diagram for a $3$-manifold/knot pair into a doubly-pointed trisection diagram for the $4$-manifold/$2$-knot pair resulting from the twist-spinning operation.

This technique offers a rich list of new manifolds that admit trisection diagrams that are amenable to study. We formulate a conjecture about $4$-manifolds with trisection genus three and provide some supporting evidence.

This work was supported by NSF grants DMS-1400543 and DMS-1758087.

Received 18 September 2017

Accepted 15 January 2018

Published 1 February 2019