SMRI Seminar: Futer -- The generalized knot complement problem

SMRI Seminar 
’The generalized knot complement problem’
Dave Futer (Temple University, Philadelphia) 

Date and time: Thursday 2 May, 13:00-14:00 AEST 
Location: Law Annex Lecture Theatre 026 and online 
Register/join for online attendance: https://uni-sydney.zoom.us/j/82819441564

Abstract: In 1908, Tietze posed the provocative question of whether a mathematical knot 
- a knotted rope, with its ends spliced together - is completely determined by the 
topological shape of the empty space that surrounds the knot. After being open for 80 
years, this question was solved in 1988, and we know the answer is Yes.

Since that time, mathematicians have studied the open question of whether the same 
property holds for knots in general 3-dimensional spaces. Given a 3-dimensional manifold 
M, is a knot in M entirely determined by the space that surrounds it in M? I will 
discuss some recent work on this question using hyperbolic (negatively curved) geometry. 
This is joint work with Jessica Purcell and Saul Schleimer.  

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Please join us after the seminar for SMRI afternoon tea, 2:00-2:45pm every Thursday on
the SMRI Terrace (accessed through A14-04-L4.36) 

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Current and past seminar info (including recordings) can be found on the seminars
webpage.  

Other upcoming SMRI events can be found here:
https://mathematical-research-institute.sydney.edu.au/news-events/ 

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