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1998 | 42 | 1 | 129-144
Tytuł artykułu

Dehn filling: A survey

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
42
Numer
1
Strony
129-144
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712-1082, U.S.A.
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