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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-4,
author = {Louis Funar and Martha Giannoudovardi and Daniele Ettore Otera},
title = {On groups with linear sci growth},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {47-62},
zbl = {06366990},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-4}
}
Louis Funar; Martha Giannoudovardi; Daniele Ettore Otera. On groups with linear sci growth. Fundamenta Mathematicae, Tome 228 (2015) pp. 47-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-4/