Topology of Asymptotic Cones and S-machine
Geometric Topology
2014-01-22 v1
Abstract
Sapir, Birget and Rips showed how to construct groups from Turing machines. To achieve such a construction they introduced the notion of S-machine. Then considering a simplified S-machine Sapir and Olshanskii showed how to construct a group such that each of its asymptotic cone is non-simply connected. Still using the notion S-machine, they constructed a group with two asymptotic cone non-homeomorphic. In this paper we show that each asymptotic cone of a group constructed following the whole method of Sapir, Birget and Rips is not simply connected.
Cite
@article{arxiv.1401.5290,
title = {Topology of Asymptotic Cones and S-machine},
author = {Anthony Gasperin},
journal= {arXiv preprint arXiv:1401.5290},
year = {2014}
}
Comments
arXiv admin note: text overlap with arXiv:math/9811105, arXiv:math/0501542 by other authors