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Trisections and spun 4-manifolds

Authors :
Meier, Jeffrey
Source :
Math. Res. Lett. 25 (2018), no. 5, 1497-1524
Publication Year :
2017

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.<br />Comment: 16 pages, 12 figures. Comments welcome!

Subjects

Subjects :
Mathematics - Geometric Topology

Details

Database :
arXiv
Journal :
Math. Res. Lett. 25 (2018), no. 5, 1497-1524
Publication Type :
Report
Accession number :
edsarx.1708.01214
Document Type :
Working Paper