Postal address: |
Dr Jonathan Hillman School of Mathematics and Statistics F07 University of Sydney NSW 2006 Australia | |
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Office: | Level 6, Room 609 Carslaw Building | |
Email: | jonathan.hillman@sydney.edu.au | |
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 2022. These incorporate new material, particularly in Chapters 4, 9, 10, 12, 16 and 18. Since then I have made further corrections and minor adjustments. The version available here was last updated on 1 December 2023. (See page xiv for a summary of the main changes, and also the Errata and Addenda for the current revision .)
My most recent (final?) book is ``Poincaré Duality in Dimension Three", which has been published by MSP as an Open Book. Since publication in 2020 I have been collating errata and new material, which I hope may soon appear in a revised version. For the moment (21 July 2023), this material may be found in Errata and Addenda, together with New Chapter 13.
Graphs, Surfaces and Knots corresponds to half of the third-year course ``Geometry and Topology".
Some questions on low dimensional topology is a list of problems in low dimensional topology, group theory and knot theory that I revisit regularly.
Aspherical 4-manifolds with elementary amenable fundamental groups grew out of discussions with Jim Davis at the MATRIX meeting on {\it Topology in Low and High Dimensions} at Creswick, Vic., in January 2019.
Locally flat embeddings of 3-manifolds in $S^4$
See also Publications