The group Out of outer automorphisms of the free group has been an object of active study for many years, yet its geometry is not well understood. Recently, effort has been focused on finding a hyperbolic complex on which Out acts, in analogy with the curve complex for the mapping class group. Here, we focus on one of these proposed analogues: the edge splitting complex ESn, equivalently known as the separating sphere complex. We characterize geodesic paths in its 1-skeleton ESn1 algebraically, and use our characterization to find lower bounds on distances between points in this graph.
1
Saint Louis University, United States
2
University of South Florida, Tampa, USA
Lucas Sabalka; Dmytro Savchuk. On the geometry of the edge splitting complex. Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 565-598. doi: 10.4171/ggd/239
@article{10_4171_ggd_239,
author = {Lucas Sabalka and Dmytro Savchuk},
title = {On the geometry of the edge splitting complex},
journal = {Groups, geometry, and dynamics},
pages = {565--598},
year = {2014},
volume = {8},
number = {2},
doi = {10.4171/ggd/239},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/239/}
}
TY - JOUR
AU - Lucas Sabalka
AU - Dmytro Savchuk
TI - On the geometry of the edge splitting complex
JO - Groups, geometry, and dynamics
PY - 2014
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UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/239/
DO - 10.4171/ggd/239
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