Gromov's knot distortion

Geometry Topology Seminar
Friday, January 28, 2011 - 2:05pm
1 hour (actually 50 minutes)
Skiles 269
Princeton University
Gromov defined the distortion of an embedding of S^1 into R^3 and asked whether every knot could be embedded with distortion less than 100.  There are (many) wild embeddings of S^1 into R^3 with finite distortion, and this is one reason why bounding the distortion of a given knot class is hard.  I will show how to give a nontrivial lower bound on the distortion of torus knots, which is sharp in the case of (p,p+1) torus knots.  I will also mention some natural conjectures about the distortion, for example that the distortion of the (2,p)-torus knots is unbounded.