Dehn filling: A survey

C. Gordon

Banach Center Publications (1998)

  • Volume: 42, Issue: 1, page 129-144
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Gordon, C.. "Dehn filling: A survey." Banach Center Publications 42.1 (1998): 129-144. <http://eudml.org/doc/208801>.

@article{Gordon1998,
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.},
author = {Gordon, C.},
journal = {Banach Center Publications},
keywords = {Dehn filling; 3-manifold},
language = {eng},
number = {1},
pages = {129-144},
title = {Dehn filling: A survey},
url = {http://eudml.org/doc/208801},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Gordon, C.
TI - Dehn filling: A survey
JO - Banach Center Publications
PY - 1998
VL - 42
IS - 1
SP - 129
EP - 144
AB - 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.
LA - eng
KW - Dehn filling; 3-manifold
UR - http://eudml.org/doc/208801
ER -

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