Classical and quantum geometry of moduli spaces in three-dimensional gravity
نویسندگان
چکیده
We describe some results concerning the phase space of 3-dimensional Einstein gravity when space is a torus and with negative cosmological constant. The approach uses the holonomy matrices of flat SL(2,R) connections on the torus to parametrise the geometry. After quantization, these matrices acquire noncommuting entries, in such a way that they satisfy q-commutation relations and exhibit interesting geometrical properties. In particular they lead to a quantization of the Goldman bracket.
منابع مشابه
60 20 07 v 3 9 F eb 1 99 6 VIRTUAL MODULI CYCLES AND GW - INVARIANTS
The study of moduli spaces plays a fundamental role in our understanding geometry and topology of algebraic manifolds, or more generally, symplectic manifolds. One example is the Donaldson theory (and more recently the Seiberg-Witten invariants), which gives rise to differential invariants of 4-manifolds [Do]. When the underlying manifold is an algebraic surface, then it is the intersection the...
متن کاملMapping Class Groups and Moduli Spaces of Curves
It is classical that there is a very strong relation between the topology of Mg, the moduli space of smooth projective curves of genus g, and the structure of the mapping class group Γg, the group of homotopy classes of orientation preserving diffeomorphisms of a compact orientable surface of genus g. The geometry of Mg, the topology of Mg, and the structure of Γg are all intimately related. Un...
متن کاملModuli Spaces in the Four-Dimensional Topological Half-Flat Gravity
We classify the moduli spaces of the four-dimensional topological half-flat gravity models by using the canonical bundle. For a K3-surface or T 4 , they describe an equivalent class of a trio of the Einstein-Kähler forms (the hyperkähler forms). We calculate the dimensions of these moduli spaces by using the Atiyah-Singer Index theorem. We mention the partition function and the possibility of t...
متن کاملCombinatorial quantisation of Euclidean gravity in three dimensions
In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat G-connections, where G is a typically non-compact Lie group which depends on the signature of space-time and the cosmological constant. For Euclidean signature and vanishing cosmological constant, G is the three-dimensional Euclidean group. For this case the Poisson struc...
متن کاملDispersion of Torsional Surface Wave in a Pre-Stressed Heterogeneous Layer Sandwiched Between Anisotropic Porous Half-Spaces Under Gravity
The study of surface waves in a layered media has their viable application in geophysical prospecting. This paper presents an analytical study on the dispersion of torsional surface wave in a pre-stressed heterogeneous layer sandwiched between a pre-stressed anisotropic porous semi-infinite medium and gravitating anisotropic porous half-space. The non-homogeneity within the intermediate layer a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005