English

Trisections and spun 4-manifolds

Geometric Topology 2022-10-19 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1708.01214,
  title  = {Trisections and spun 4-manifolds},
  author = {Jeffrey Meier},
  journal= {arXiv preprint arXiv:1708.01214},
  year   = {2022}
}

Comments

16 pages, 12 figures. Comments welcome!

R2 v1 2026-06-22T21:05:58.329Z