Geodesic
On groups with linear sci growth
Louis Funar 1   ; Martha Giannoudovardi 2   ; Daniele Ettore Otera 3
1 Institut Fourier BP 74, UMR 5582, UniversitéGrenoble I 38402 Saint-Martin-d'Hères Cedex, France
2 Department of Mathematics University of Athens 157 84 Athens, Greece
3 Institute of Mathematics and Informatics Vilnius University Akademijos st. 4 LT-08663, Vilnius, Lithuania
Fundamenta Mathematicae, Tome 228 (2015) no. 1, pp. 47-62 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove that the semistability growth of hyperbolic groups is linear, which implies that hyperbolic groups which are sci (simply connected at infinity) have linear sci growth. Based on the linearity of the end-depth of finitely presented groups we show that the linear sci is preserved under amalgamated products over finitely generated one-ended groups. Eventually one proves that most non-uniform lattices have linear sci.
DOI : 10.4064/fm228-1-4
Keywords: prove semistability growth hyperbolic groups linear which implies hyperbolic groups which sci simply connected infinity have linear sci growth based linearity end depth finitely presented groups linear sci preserved under amalgamated products finitely generated one ended groups eventually proves non uniform lattices have linear sci

Louis Funar  1   ; Martha Giannoudovardi  2   ; Daniele Ettore Otera  3

1 Institut Fourier BP 74, UMR 5582, UniversitéGrenoble I 38402 Saint-Martin-d'Hères Cedex, France
2 Department of Mathematics University of Athens 157 84 Athens, Greece
3 Institute of Mathematics and Informatics Vilnius University Akademijos st. 4 LT-08663, Vilnius, Lithuania 
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Louis Funar; Martha Giannoudovardi; Daniele Ettore Otera. On groups with linear sci growth. Fundamenta Mathematicae, Tome 228 (2015) no. 1, pp. 47-62. doi: 10.4064/fm228-1-4

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