caa a22 4500 445386045 CHVBK 20180317143032.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s10714-010-0981-9 doi (NATIONALLICENCE)springer-10.1007/s10714-010-0981-9 Meusburger C. Department Mathematik, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany aut Geometry and observables in (2+1)-gravity [Elektronische Daten] [C. Meusburger] We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover by holonomies. We explain how this description can be used to clarify the geometrical interpretation of the fundamental physical variables of the theory, holonomies and Wilson loops. In particular, we discuss the role of Wilson loop observables as the generators of the two fundamental transformations that change the geometry of (2+1)-spacetimes, grafting and earthquake. We explain how these variables can be determined from realistic measurements by an observer in the spacetime. Springer Science+Business Media, LLC, 2010 General relativity nationallicence Quantum gravity nationallicence Three-dimensional gravity nationallicence Teichmüller geometry nationallicence Wilson loops nationallicence General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/9(2011-09-01), 2409-2420 0001-7701 43:9<2409 2011 43 10714 https://doi.org/10.1007/s10714-010-0981-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-010-0981-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Meusburger C. Department Mathematik, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/9(2011-09-01), 2409-2420 0001-7701 43:9<2409 2011 43 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer