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RESEARCH BLOG 3/18/03 I've added a page on unknots , with some examples of Haken, and a

Summary: RESEARCH BLOG 3/18/03
I've added a page on unknots , with some examples of Haken, and a
link to Marc Culler's computer program Gridlink, which allows one to
untangle a link using Dynnikov's algorithm. If you have any good ex-
amples of unknot projections, please send them to me and I'll add them
to the page. Dynnikov came to visit here in February, and hopefully
I'll discuss at some point what questions we were thinking about.
I'm going to Lubbock, Texas for the spring topology and dynamical
systems conference tomorrow. My talk will be a survey on algorithms
in 3-manifold topology. Of course, like any survey, I will leave out more
than I discuss, such as algorithms for quantum invariants and the word
problem for fundamental groups of 3-manifolds.
The principle goal of 3-manifold topology can be considered to clas-
sify 3-manifolds up to homeomorphism. One notion of classification
is algorithmic: given two compact 3-manifolds, presented as simplicial
complexes, is there an algorithm to tell whether or not the manifolds
are homeomorphic? This question is unsolvable for four-dimensional
manifolds or higher, and is solved for surfaces, so three dimensions
is the remaining unknown case. Given the difficulty of this problem,
one may try to find invariants of three manifolds, which might not be


Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago


Collections: Mathematics