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 |
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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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