J. Hillman

activity

20022023

most citedOn reciprocality of twisted Alexander invariants

23 citations · 126 across the 39 of their papers we have counts for

collaborators

42 papers

math.GT2023

Homotopy types of 4-manifolds with 3-manifold fundamental groups

Jonathan A. Hillman

We show that the homotopy type of a 4-manifold $M$ whose fundamental group is a finitely presentable $P D_{3}$ -group $π$ and with $w_{1} (M) = w_{1} (π)$ is determined by $π$ , $π_{2} (M)$ , $k_1(…

math.GT2023

The groups of branched twist-spun knots

Jonathan A. Hillman

We characterize the groups of branched twist spins of classical knots in terms of 3-manifold groups, and also give a purely algebraic, conjectural characterization in terms of $PD_…

math.GR2023

Non-solvable torsion-free virtually solvable groups

Jonathan A. Hillman

There are perfect Bieberbach groups of Hirsch length 15, but none in lower dimensions. We shall show that a nonsolvable, torsion free, virtually solvable group $S$ must have Hirsch…

math.GT2022

Pro- $p$ completions of $P D_{n}$ -groups

Jonathan Hillman, Dessislava H. Kochloukova

We sharpen earlier work on the pro- $p$ completions of orientable $P D_{3}$ -groups. There are four cases, and we give examples of aspherical 3-manifolds representing each case. In thre…

math.GT2021

Centralizers of torsion in 3-manifold groups

Jonathan A. Hillman

We show that if $P$ is a $P D_{3}$ -complex and $g \in π_{1} (P)$ has finite order $> 1$ and infinite centraliser then $π_{1} (P)$ retracts onto $Z /2 Z \oplus Z$ . If $P$ is an irreducible…

math.GT2021

$P D_{3}$ -complexes bound

Jonathan A. Hillman

We show that every $P D_{3}$ -complex $P$ bounds a $P D_{4}$ -pair $(Z, P)$ . If $P$ is orientable we may assume that $π_{1} (Z) = 1$ . We show also that if $P$ has a manifold 1-skeleton then it i…

Homotopy types of 4-manifolds with 3-manifold fundamental groups

The groups of branched twist-spun knots

Non-solvable torsion-free virtually solvable groups

Pro-p completions of PDn​-groups

Centralizers of torsion in 3-manifold groups

PD3​-complexes bound

Pro- $p$ completions of $P D_{n}$ -groups

$P D_{3}$ -complexes bound