J. Hillman

activity

20242026

collaborators

6 papers

math.GR2026

Aspherical $P D_{4}$ -pairs

James F. Davis, J. A Hillman

This is the third of three related preprints. We consider here which groups $π$ and $P D_{3}$ -complexes $Y$ are realised by $P D_{4}$ -pairs $(X, Y)$ with $X$ aspherical and $π_{1} X ≅ π$ ,…

math.GT2025

3-manifolds with more than one abelian embedding

Jonathan A. Hillman

We construct 3-manifolds which have at least two inequivalent embeddings such that both complementary regions have abelian fundamental group.

math.GT2025

Aspherical 4-manifolds with elementary amenable fundamental group

James F. Davis, J. A. Hillman

We classify the possible elementary amenable fundamental groups of compact aspherical 4-manifolds with boundary and conclude that they are either polycyclic or solvable Baumslag- S…

math.GT2025

Aspherical manifolds with boundary

James F. Davis, J. A. Hillman

We undertake a systematic investigation of compact aspherical manifolds with boundary; motivated by the plethora of examples in the bounded case and by the beauty of the theory in…

math.GT2024

The $F_{2}$ -cohomology rings of 3-manifolds

Jonathan A. Hillman

We give a new argument for the characterization of the cohomology rings of closed 3-manifolds with coefficients $F_{2}$ , first given by M. M. Postnikov (in terms of intersec…

math.GT2024

Locally flat embeddings of 3-manifolds in $S^{4}$

J. A. Hillman

M. Freedman showed that every homology 3-sphere embeds as a locally flat submanifold of $S^{4}$ . This is in striking contrast to the state of our knowledge of smooth embeddings of ho…

Aspherical PD4​-pairs

3-manifolds with more than one abelian embedding

Aspherical 4-manifolds with elementary amenable fundamental group

Aspherical manifolds with boundary

The F2​-cohomology rings of 3-manifolds

Locally flat embeddings of 3-manifolds in S4

Aspherical $P D_{4}$ -pairs

The $F_{2}$ -cohomology rings of 3-manifolds

Locally flat embeddings of 3-manifolds in $S^{4}$