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Mosc. Math. J., 2014, Volume 14, Number 4, Pages 645–667 (Mi mmj539)  

Poincaré's polyhedron theorem for cocompact groups in dimension $4$

Sasha Anan'ina, Carlos H. Grossia, Júlio C. C. da Silvab

a Departamento de Matemática, ICMC, Universidade de São Paulo, Caixa Postal 668, 13560-970—São Carlos—SP, Brasil
b Departamento de Matemática, IMECC, Universidade Estadual de Campinas, 13083-970—Campinas—SP, Brasil

Abstract: We prove a version of Poincaré's polyhedron theorem whose requirements are as local as possible. New techniques such as the use of discrete groupoids of isometries are introduced. The theorem may have a wide range of applications and can be generalized to the case of higher dimension and other geometric structures. It is planned as a first step in a program of constructing compact $\mathbb C$-surfaces of general type satisfying $c_1^2=3c_2$.

Key words and phrases: Poincaré's polyhedron theorem, discrete groups, geometric structures on manifolds, compact $\mathbb C$-surfaces of general type.

DOI: https://doi.org/10.17323/1609-4514-2014-14-4-645-667

Full text: http://www.mathjournals.org/.../2014-014-004-001.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 22E40; Secondary 14J29, 20L05
Received: October 29, 2013; in revised form December 14, 2013
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Citation: Sasha Anan'in, Carlos H. Grossi, Júlio C. C. da Silva, “Poincaré's polyhedron theorem for cocompact groups in dimension $4$”, Mosc. Math. J., 14:4 (2014), 645–667

Citation in format AMSBIB
\Bibitem{AnaGroDa 14}
\by Sasha~Anan'in, Carlos~H.~Grossi, J\'ulio~C.~C.~da Silva
\paper Poincar\'e's polyhedron theorem for cocompact groups in dimension~$4$
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 4
\pages 645--667
\mathnet{http://mi.mathnet.ru/mmj539}
\crossref{https://doi.org/10.17323/1609-4514-2014-14-4-645-667}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3292044}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000349324800001}


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