Proceedings - Mathematical Sciences

, Volume 120, Issue 2, pp 217–241 | Cite as

Splittings of free groups, normal forms and partitions of ends

  • Siddhartha GadgilEmail author
  • Suhas Pandit


Splittings of a free group correspond to embedded spheres in the 3-manifold M = # k S 2 × S 1. These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in π 2(M) can be represented by an embedded sphere.


Free groups sphere complex algebraic intersection numbers graphs of trees 


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Copyright information

© Indian Academy of Sciences 2010

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Department of MathematicsIndian Institute of Science Education and ResearchPuneIndia

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