It is well known that given a diagram of a knot \\(K\\) wit h \\(n\\) crossings\, one can construct a\ntriangulation of \\(S^3 - K\\) with at most \\(4n\\) tetrahedra. A natural question is then: given a tri angulation of a knot complement with \\(t\\) tetrahedra\, is the minimum c rossing number (for a diagram) of K bounded by a linear or polynomial func tion in \\(t\\)? We will answer the question in the negative by construct ing a family of hyperbolic knot complements where for each knot \\(K_n\\) in \\(S^3\\) whose the minimum crossing number goes as a function of \\(O( b^n)\\) for \\(b > 1\\)\, but the minimum number of tetrahedra in a triang ulation of \\(S^3 - K_n\\) is bounded above by \\(O(n)\\). Similar constr uctions exist for torus and satellite knot complements.\n\n
This is join t work with Robert Haraway.\n LOCATION:https://researchseminars.org/talk/GaTO/5/ END:VEVENT END:VCALENDAR