Volume 11, issue 2 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Totally geodesic surfaces with arbitrarily many compressions

Pradthana Jaipong

Algebraic & Geometric Topology 11 (2011) 643–654
Abstract

A closed totally geodesic surface in the figure eight knot complement remains incompressible in all but finitely many Dehn fillings. In this paper, we show that there is no universal upper bound on the number of such fillings, independent of the surface. This answers a question of Ying-Qing Wu.

Keywords
totally geodesic surface, figure eight knot, Dehn filling
Mathematical Subject Classification 2000
Primary: 57N10, 57N25
Secondary: 57N50
References
Publication
Received: 3 September 2010
Revised: 7 November 2010
Accepted: 13 December 2010
Published: 24 February 2011
Authors
Pradthana Jaipong
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green Street
Urbana IL 61801
USA
Department of Mathematics
Science Faculty
Chiangmai University
Chiangmai 50200
Thailand