J. Hillman

activity

20042021

most cited

S o l^{3} \times E^{1}

-manifolds

2 citations · 4 across the 6 of their papers we have counts for

collaborators

Showing math.GTShow all

6 papers · 1 filter

math.GT2021

Nilpotent groups with balanced presentations. II

J. A. Hillman

If $G$ is a nilpotent group with a balanced presentation and $G \neq ≅ Z^{3}$ then $β_{1} (G; Q) \leq 2$ \cite{Hi22}. We show that if such a group $G$ has an abelian nor…

math.GT2021

Subnormality in $P D_{3}$ -groups and $L^{2}$ -Betti numbers

J. A. Hillman

We reconsider work of Elkalla on subnormal subgroups of 3-manifold groups, giving essentially algebraic arguments that extend to the case of $P D_{3}$ -groups and group pairs. However…

math.GT2013★ 2 cited

$S o l^{3} \times E^{1}$ -manifolds

J. A. Hillman

We show that $S o l^{3} \times E^{1}$ -manifolds are Seifert fibred, with general fibre the torus, and base one of the seven flat 2-orbifolds $T, Kb, \mathbb{A}, \mathbb{M…

math.GT2011

An infrasolvmanifold which does not bound

J. A. Hillman

Every 4-dimensional infrasolvmanifold $M$ with $β_{1} (M; Q) > 0$ or which is flat or has one of the geometries $N i l^{4}$ , $S o l_{m, n}^{4}$ , or $S o l_{0}^{4}$ b…

math.GT2011★ 1 cited

Parallelizability of 4-dimensional infrasolvmanifolds

J. A. Hillman

We show that if $M$ is an orientable 4-dimensional infrasolvmanifold and either $β = β_{1} (M; Q) \geq 2$ or $M$ is a $S o l_{0}^{4}$ - or a $S o l_{m, n}^{4}$ -manifold (wit…

math.GT2004★ 1 cited

Surgery on $SL \times E^{n}$ -manifolds

J. A. Hillman, S. K. Roushon

We show that although closed $SL \times E^{n}$ -manifolds do not admit metrics of nonpositive sectional curvature, the arguments of Farrell and Jones can be exte…

Nilpotent groups with balanced presentations. II

Subnormality in PD3​-groups and L2-Betti numbers

Sol3×E1-manifolds

An infrasolvmanifold which does not bound

Parallelizability of 4-dimensional infrasolvmanifolds

Surgery on SL×En-manifolds

Subnormality in $P D_{3}$ -groups and $L^{2}$ -Betti numbers

$S o l^{3} \times E^{1}$ -manifolds

Surgery on $SL \times E^{n}$ -manifolds