000			02099n a2200265#a 4500
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007			cr cuuuuuauuuu
008			150202s2015 bl por d
035			_aocm51338542
040			_aP5A _cP5A
090			_acs
100	1		_aParlier, Hugo. _u(University of Fribourg, Suiça) _96760
245	1	0	_aCombinatorial moduli spaces.
260			_aRio de Janeiro: _bIMPA, _c2015.
300			_avideo online
505	2		_aCombinatorial spaces, often related to simple closed curves on surfaces, have been used in different ways to understand Teichmüller spaces, mapping class groups and moduli spaces. More specifically, the curve and pants graphs have been helpful tools to understand geometric properties of Teichmüller spaces with its different metrics and the mapping class group. Flip graphs are other examples of useful combinatorial spaces. The vertices of these graphs are isotopy classes of triangulations and two triangulations share an edge if they are related by a flip (or equivalently differ by a single arc). Flip graphs are also conveniently quasi-isometric to the underlying mapping class groups. The flip graph of a polygon, although finite, has been particularly well studied, most famously by Sleator, Tarjan and Thurston who studied its diameter. In another piece of work, they studied the diameters of flip graphs of punctured spheres (this time up to the action of their mapping class groups) .
650	0	4	_aMatematica. _2larpcal _919899
697			_aCongressos e Seminários. _923755
711	2		_aHyperbolic Geometry and Minimal Surfaces _d(2015: _cIMPA, Rio de Janeiro, Brazil) _96755
856	4		_zVIDEO _uhttps://www.youtube.com/watch?v=S-vZnuiNYjY&list=PLo4jXE-LdDTSse0dM2KDQFGXqPMkAQNaf&index=9
856	4		_zRESUMOS _uhttps://impa.br/wp-content/uploads/2016/12/abstracts.pdf
942			_2ddc _cBK
999			_aCOMBINATORIAL moduli spaces. Rio de Janeiro: IMPA, 2015. video online. Disponível em: <https://www.youtube.com/watch?v=S-vZnuiNYjY&list=PLo4jXE-LdDTSse0dM2KDQFGXqPMkAQNaf&index=9>. Acesso em: 2 fev. 2015. _c34922 _d34922