Splittings of free groups, normal forms and partitions of ends

Gadgil, Siddhartha and Pandit, Suhas (2010) Splittings of free groups, normal forms and partitions of ends. In: Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 120 (2). pp. 217-241.

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Abstract

Splittings of a free group correspond to embedded spheres in the 3-manifold M = # (k) S (2) x 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 pi (2)(M) can be represented by an embedded sphere.

Item Type:	Journal Article
Publication:	Proceedings of the Indian Academy of Sciences - Mathematical Sciences
Publisher:	Indian Academy of Sciences
Additional Information:	Copyright of this article belongs to Indian Academy of Sciences.
Keywords:	Free groups; sphere complex; algebraic intersection numbers; graphs of trees.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	20 Sep 2010 09:41
Last Modified:	20 Sep 2010 09:41
URI:	http://eprints.iisc.ac.in/id/eprint/32247

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