RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mosc. Math. J.: Year: Volume: Issue: Page: Find

 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

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
Language:

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}