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Geometriae Dedicata

, Volume 158, Issue 1, pp 211–234 | Cite as

Geosphere laminations in free groups

  • Siddhartha GadgilEmail author
  • Suhas Pandit
Original Paper
  • 82 Downloads

Abstract

We construct geosphere laminations for free groups, which are codimension one analogues of geodesic laminations on surfaces. Other analogues that have been constructed by several authors are dimension-one instead of codimension-one. Our main result is that the space of such laminations is compact. This in turn is based on the result that crossing, in the sense of Scott-Swarup, is an open condition. Our construction is based on Hatcher’s normal form for spheres in the model manifold.

Keywords

Free groups Laminations Splittings Scott-Swarup intersection numbers 

Mathematics Subject Classification (2000)

57M05 57M07 20E06 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Max-Planck Institute for MathematicsBonnGermany

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