Title: Length spectrum of a hyperbolic 3-manifold
Abstract: Every geodesic in hyperbolic 3-manifold has a naturally defined
complex length. All geodesics in a manifold can be ordered by their length
lexicographically and create a length spectrum. There is a one-to-one
correspondence between fundamental group of a hyperbolic 3-manifold and its
length spectrum. In the first part of the talk we will describe some facts
about length and ortholength spectra of hyperbolic 3-manifolds and
demonstrate the working algorithm for the spectra. In the second part we'll
consider applications of this algorithm to the proof of Exceptional
Manifolds Conjecture and Dehn parental test.