Colloquium: David Futer (Temple University)


Event Details


Title: Effective hyperbolic geometry

Abstract: Powerful the­o­rems of Thurston, Perel­man, and Mostow tell us that al­most every 3-di­men­sion­al man­i­fold ad­mits a hy­per­bol­ic met­ric, and that this met­ric is unique. Thus, in prin­ci­ple, there is a 1-to-1 cor­re­spon­dence be­tween a com­bi­na­to­r­i­al de­scrip­tion of a 3-man­i­fold and its geom­e­try. The ex­is­tence of this 1-to-1 cor­re­spon­dence has been known, at least con­jec­tural­ly, for over 30 years. On the oth­er hand, only in the last few years have we be­gun to see the out­lines of a con­crete dic­tio­nary be­tween com­bi­na­to­r­i­al fea­tures and geo­met­ric mea­sure­ments. I will sur­vey some of what is known and un­known, pay­ing spe­cial at­ten­tion to the problem of estimating the volume of a knot complement in the 3-sphere.