Dr Jonathan Hillman|
School of Mathematics and Statistics F07
University of Sydney NSW 2006
|Office:||Room 617 Carslaw Building|
|Telephone:||+61 2 9351 5775|
|Department Fax:||+61 2 9351 4534|
Although I am now retired, and am no longer involved in supervising candidates for higher degrees, 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).
Four-Manifolds, Geometries and Knots (Geometry and Topology Monographs, vol. 5, Geometry and Topology Publications, December 2002) 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 subgroups of the fundamental group and in deriving the results on 2-knot groups from the work on 4-manifolds.
Revisions were made available through GT in 2007 and 2014. These incorporate new material, particularly in Chapters 4, 9, 10, 12, 16 and 18, and corrections to all the errors and typos found up to [30 June 2014]. See page xiv for a summary of the main changes. The version available here was last updated on 22 February 2017; in particular Chapter 15 has been rewritten, to include new work completing the determination of virtually solvable 2-knot groups. (See also the Errata for the 2014 revision, begun 14 July 2014).
Graphs, Surfaces and Knots corresponds to half of the third-year course ``Geometry and Topology".
Poincar\'e duality in low dimensions are the background notes for a four-lecture hour minicourse given in Agua de Lindoias, S.P., Brazil (29 July -- 3 August, 2012), and repeated (with a somewhat different presentation) in Chicago (April 2014).
Some questions on low dimensional topology is a list of problems in low dimensional topology, group theory and knot theory that I revisit regularly.
See also Publications