L Reeves, P Scott and G A Swarup

JSJ Decompositions of Poincare Duality Pairs

About the Book

Poincaré Duality groups and pairs have been studied by several authors since their introduction by R.Bieri, Frank Johnson, C.T.C. Wall and others in the early 1970s. Their relations to group theory, as well as to manifold theory, were discussed by Mike Davis in a survey article which appeared in 2000. These notes continue the study of Poincare Duality Groups and pairs in a different direction. The authors show that the analogues of Jaco-Shalen-Johannson Decomposition hold for Poincare Duality Pairs. Specialising to three dimensions, they further show that the components of the characteristic submanifold are the same as in the three manifold case and also prove an analogue of Johannson’s Deformation Theorem for Poincare Duality Pairs in dimension three. It is known from the work of B. Eckmann, H. Muller and P. Linnell  that in dimension two, Poincare Duality groups are the same as surface groups. The results in these notes and results of M. Kapovich  B. Kleiner  on Coarse Alexander Duality provide some steps towards a similar result in three dimensions.

About the Authors

Lawrence Reeves is at the University of Melbourne, and was previously at Aix-Marseille University.

Anandaswarup Gadde has worked in several universities, mainly TFR Mumbai and the University of Melbourne, from where he retired in 2005.

Peter Scott worked at the University of Michigan in Anne Arbor, after previously working at the University of Liverpool.

Managing Editors

  • Colin Adams
  • Eric Friedlander
  • Sergei Tabachnikov

Editorial Board

  • George Andrews
  • Colin Adams
  • Eric Friedlander
  • Robert Ghrist
  • Joel Hass
  • Robion Kirby
  • Alex Kontorovich
  • Sergei Tabachnikov

AMR Research Monographs
Volume 3

ISBN: 978-1-959384-03-8


Books in the AMR Book Series are available for download without charge.  To download a copy, click on the cover image of the book, or on the download button above.


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.