Jonathan Hillman

Honorary Reader in the School of Mathematics and Statistics at the University of Sydney.

Postal address:	Dr Jonathan Hillman School of Mathematics and Statistics F07 University of Sydney NSW 2006 Australia
Office:	Room 617 Carslaw Building
Email:	`jonh@maths.usyd.edu.au`
Telephone:	+61 2 9351 3049
Department Fax:	+61 2 9351 4534

Research Interests

I am interested in applications of algebra to low dimensional topology, (2-complexes, 3- and 4-manifolds) and knots and links (in all dimensions). I am particularly interested in the interactions between the fundamental group and Poincaré duality. In particular, I believe that all 3-dimensional Poincaré duality groups are 3-manifold groups, although I cannot yet prove this. (See Some questions on subgroups of 3-dimensional Poincaré duality groups for a problem list motivated by what is known for 3-manifold groups).

Although I am now retired, I remain a member of the Geometry and Topology group.

For one characterization of "Reader" (at an older university) see ``The Gaudy" by J.I.M.Stewart (page 218 in the Methuen paperback edition).

Recent Papers

Algebraic Invariants of Links (World Scientific Publishing Co, x+305pp, October 2002) is intended to replace my 1981 notes as an introduction to links and a reference for the invariants of abelian coverings of link exteriors, and to outline more recent work, particularly that related to free coverings, nilpotent quotients and concordance. The table of contents, Preface and Chapter 1 are available here as a gzipped .ps file. See also the Errata and Addenda (begun 27 November 2002).

Four-Manifolds, Geometries and Knots (Geometry and Topology Monographs, vol. 5, Geometry and Topology Publications, December 2002, xiv+379 pp) is based on my 1989 and 1994 monographs on 2-knots and on geometric 4-manifolds. However the arguments have been improved in many cases, notably in using Bowditch's homological criterion for virtual surface groups to streamline the results on surface bundles, using $L^2$-methods instead of localization, completing the characterization of mapping tori, relaxing the hypotheses on torsion or on abelian normal subgroups in the fundamental group and in deriving the results on 2-knot groups from the work on 4-manifolds. (It is available here as a gzipped .ps file, xii+280pp.) See also the Errata and Addenda (begun 20 March 2003).

An updated version (current version) is now available (as a .pdf file). This includes new material, particularly in Chapters 4, 9 and 10, and corrections to all the errors and typos found up to [12 December 2011]. See page xiv for a summary of the main changes. The pagination is the same as the 2002 GT version, except that there are 2 more pages of references. See also the Errata for the 2007 revision (begun 19 November 2007).

Publications