15 research outputs found
On a problem of A. Weil
A topological invariant of the geodesic laminations on a modular surface is
constructed. The invariant has a continuous part (the tail of a continued
fraction) and a combinatorial part (the singularity data). It is shown, that
the invariant is complete, i.e. the geodesic lamination can be recovered from
the invariant. The continuous part of the invariant has geometric meaning of a
slope of lamination on the surface.Comment: to appear Beitr\"age zur Algebra und Geometri
Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
In three spacetime dimensions, general relativity drastically simplifies,
becoming a ``topological'' theory with no propagating local degrees of freedom.
Nevertheless, many of the difficult conceptual problems of quantizing gravity
are still present. In this review, I summarize the rather large body of work
that has gone towards quantizing (2+1)-dimensional vacuum gravity in the
setting of a spatially closed universe.Comment: 61 pages, draft of review for Living Reviews; comments, criticisms,
additions, missing references welcome; v2: minor changes, added reference
A glimpse into Thurston's work
We present an overview of some significant results of Thurston and their
impact on mathematics. The final version of this paper will appear as Chapter 1
of the book "In the tradition of Thurston: Geometry and topology", edited by K.
Ohshika and A. Papadopoulos (Springer, 2020)
The Double Limit Theorem and Its Legacy
International audienceThis chapter surveys recent and less recent results on convergence of Kleinian representations, following Thurston's Double Limit and "AH(acylindrical) is compact" Theorems