J. Hillman

activity

20142026

P D_{3}

-complexes

2 citations · 2 across the 5 of their papers we have counts for

collaborators

6 papers

math.GT2026

$P D_{4}$ -complexes with $π_{2}$ a projective $Z [π_{1}]$ -module

Jonathan A. Hillman

Let $X$ be a $P D_{4}$ -complex and let $π = π_{1} (X)$ . If $π$ is torsion-free and $π_{2} (X)$ is a finitely generated projective $Z [π]$ -module then either $π$ is free or $π$ is $F P$ …

math.GT2026

Aspherical $P D_{3}$ -pairs

Jonathan A. Hillman

We extend two results known for aspherical 3-manifolds to $P D_{3}$ -pairs $(P, \partial P)$ with aspherical ambient space $P$ . Every such $P D_{3}$ -pair may be assembled by attaching 1-h…

math.GT2026

On sections of Lefschetz fibrations and bundles over 2-complexes

Jonathan A. Hillman, Riccardo Pedrotti

We address the question of existence of sections of fibrations in two settings. First, we show that a bundle with base a finite 2-complex admits a section if and only if the inclus…

math.GR2020

Nilpotent groups with balanced presentations

J. A. Hillman

We show that if a torsion free nilpotent group $G$ has a balanced presentations and Hirsch length $h (G) > 3$ then $β_{1} (G; Q) = 2$ . There is just one such group which is torsion…

math.GT2016

Solvable normal subgroups of 2-knot groups

J. A. Hillman

If $X$ is an orientable, strongly minimal $P D_{4}$ -complex and $π_{1} (X)$ has one end then it has no nontrivial locally-finite normal subgroup. Hence if $π$ is a 2-knot group then (a)…

math.GT2014★ 2 cited

Indecomposable non-orientable $P D_{3}$ -complexes

J. A. Hillman

We show that the orientable double covering space of an indecomposable non-orientable $P D_{3}$ -complex has torsion free fundamental group.

PD4​-complexes with π2​ a projective Z[π1​]-module

Aspherical PD3​-pairs

On sections of Lefschetz fibrations and bundles over 2-complexes

Nilpotent groups with balanced presentations

Solvable normal subgroups of 2-knot groups

Indecomposable non-orientable PD3​-complexes

$P D_{4}$ -complexes with $π_{2}$ a projective $Z [π_{1}]$ -module

Aspherical $P D_{3}$ -pairs

Indecomposable non-orientable $P D_{3}$ -complexes