Free actions on surfaces that do not extend to arbitrary actions on 3-manifolds
- Award ID(s):
- 2313766
- PAR ID:
- 10470264
- Publisher / Repository:
- Académie des sciences, Institute de France
- Date Published:
- Journal Name:
- Comptes Rendus. Mathématique
- Volume:
- 360
- Issue:
- G2
- ISSN:
- 1778-3569
- Page Range / eLocation ID:
- 161 to 167
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
We address the following natural extension problem for group actions: Given a group [Formula: see text], a subgroup [Formula: see text], and an action of [Formula: see text] on a metric space, when is it possible to extend it to an action of the whole group [Formula: see text] on a (possibly different) metric space? When does such an extension preserve interesting properties of the original action of [Formula: see text]? We begin by formalizing this problem and present a construction of an induced action which behaves well when [Formula: see text] is hyperbolically embedded in [Formula: see text]. Moreover, we show that induced actions can be used to characterize hyperbolically embedded subgroups. We also obtain some results for elementary amenable groups.more » « less
An official website of the United States government

