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.
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
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