Geometry & Topology Seminar

Geometry & Topology Seminar 

Date: Wednesday, 14 October 2026 

Time: 12noon-1pm 

Speaker: Will Hobkirk (The University of Sydney) 

Location: SMRI Seminar Room (Macleay A12 Room 301) 

Title: $\mathbb{Z}_3$-folded surfaces and the complexity of lens spaces 

Abstract: In this talk, we introduce $\mathbb{Z}_3$-folded surfaces -- geometric
representatives of classes in $H_2(M;\mathbb{Z}_3)$ for a $3$-manifold $M$.  We define
the $\mathbb{Z}_3$-Thurston “norm”, which measures the minimum complexity of these
representatives.  This function generalises the $\mathbb{Z}_2$-Thurston norm and
provides information about triangulations of $M$.  We determine the
$\mathbb{Z}_3$-Thurston norm for the family of lens spaces $L(3n,1)$, uncovering some
interesting properties of $\mathbb{Z}_3$-folded surfaces along the way.  As a corollary,
we show that any triangulation of $L(3n,1)$ must have at least $n$ tetrahedra.  A
refinement of this approach determines the exact minimum number of tetrahedra required
to triangulate these spaces, in forthcoming joint work with Jonathan Spreer.