You are here:
  1. University of Vienna
  2. PHAIDRA
  3. Detail o:2132480
Open in new window
Title (eng)
Asymptotic cones of snowflake groups and the strong shortcut property
Author
Christopher Cashen
Author
Nima Hoda
Ecole normale supérieure, Université PSL
Author
Daniel Woodhouse
University of Oxford
Description (eng)
We exhibit an infinite family of snowflake groups all of whose asymptotic cones are simply connected. Our groups have neither polynomial growth nor quadratic Dehn function, the two usual sources of this phenomenon. We further show that each of our groups has an asymptotic cone containing an isometrically embedded circle or, equivalently, has a Cayley graph that is not strongly shortcut. These are the first examples of groups whose asymptotic cones contain ‘metrically nontrivial’ loops but no topologically nontrivial ones.
Keywords (eng)
snowflake group, asymptotic cone, shortcut group, strongly shortcut group
Subject (eng)
ÖFOS 2012 -- 101 -- Mathematics
Type (eng)
journal article
Language
[eng]
Persistent identifier
https://phaidra.univie.ac.at/o:2132480
Association (eng)
Faculty of Mathematics
License
All rights reserved