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Title

Dehn filling: A survey

Authors 1

Affiliations

  1. Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712-1082, U.S.A.

Abstract

In this paper we give a brief survey of the present state of knowledge on exceptional Dehn fillings on 3-manifolds with torus boundary. For our discussion, it is necessary to first give a quick overview of what is presently known, and what is conjectured, about the structure of 3-manifolds. This is done in Section 2. In Section 3 we summarize the known bounds on the distances between various kinds of exceptional Dehn fillings, and compare these with the distances that arise in known examples. In Section 4 we make some remarks on the special case of complements of knots in the 3-sphere. We have chosen to phrase questions as conjectures; this gives them a certain edge and perhaps increases the likelihood that someone will try to (dis)prove them. Incidentally, no particular claim is made for unattributed conjectures; most of them are lore to the appropriate folk. Related survey articles are [Go1] and [Lu]. I would like to thank Pat Callahan, Craig Hodgson, John Luecke, Alan Reid and Eric Sedgwick for helpful conversations, and the referee for his useful comments.

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Banach Center Publications
1998/42/1
Export to PBN, Opens in new tab
Pages:
129-144
Main language of publication
English
Published
1998
Exact and natural sciences