Celebratio Mathematica — Gordon — Working with Cameron

Working with Cameron: from exceptional surgeries to the L-space conjecture

Works connected to Paweł Traczyk

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C. M. Gordon: “Dehn filling: A survey,” pp. 129–144 in Knot theory (Warsaw, 13 July–17 August 1995). Edited by V. F. R. Jones, J. Kania-Bartoszyńska, J. Przytycki, P. Traczyk, and V. G. Turaev. Banach Center Publications 42. Polish Academy of Sciencies, Institute of Mathematics (Warsaw), 1998. MR 1634453 Zbl 0916.57016 incollection

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 [Gordon 1991] and [Luecke 1995].

Vaughan F. R. Jones	Related	Volume
Józef Henryk Przytycki	Related
Joanna Kania-Bartoszyńska	Related
Paweł Traczyk	Related
Vladimir G. Turaev	Related