scholarly journals Isometry group of Lorentz manifolds: A coarse perspective

2021 ◽  
Author(s):  
Charles Frances
Keyword(s):  
Isometry Group ◽  
Lorentz Manifolds

scholarly journals Actions of discrete groups on stationary Lorentz manifolds

2013 ◽  
Vol 34 (5) ◽  
pp. 1640-1673 ◽  
Author(s):  
PAOLO PICCIONE ◽  
ABDELGHANI ZEGHIB
Keyword(s):  
Vector Field ◽  
Isometry Group ◽  
Killing Vector ◽  
Connected Components ◽  
Discrete Groups ◽  
Killing Vector Field ◽  
Finite Cover ◽  
Lorentzian Manifolds ◽  
Lorentz Manifolds ◽  
Amalgamated Products

AbstractWe study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated products) of a flat Lorentzian torus and a compact Riemannian (respectively, lightlike) manifold.

scholarly journals On Polish groups admitting non-essentially countable actions

2020 ◽  
pp. 1-15
Author(s):  
ALEXANDER S. KECHRIS ◽  
MACIEJ MALICKI ◽  
ARISTOTELIS PANAGIOTOPOULOS ◽  
JOSEPH ZIELINSKI
Keyword(s):  
Equivalence Relation ◽  
Isometry Group ◽  
Alternative Proof ◽  
Orbit Equivalence ◽  
Locally Compact ◽  
Continuous Action ◽  
Polish Groups ◽  
Infinite Dimensional ◽  
Open Question ◽  
New Criterion

Abstract It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. We answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space. This class contains all non-archimedean Polish groups, for which we provide an alternative proof based on a new criterion for non-essential countability. Finally, we provide the following variant of a theorem of Solecki: every infinite-dimensional Banach space has a continuous action whose orbit equivalence relation is Borel but not essentially countable.

scholarly journals The isometry group of Outer Space

2012 ◽  
Vol 231 (3-4) ◽  
pp. 1940-1973 ◽  
Author(s):  
Stefano Francaviglia ◽  
Armando Martino
Keyword(s):  
Isometry Group ◽  
Outer Space
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