Discrete subgroups of the isometry group of the plane and tilings

2012 ◽  
pp. 85-97
Author(s):  
A. Sossinsky
Keyword(s):  
Isometry Group ◽  
Discrete Subgroups

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

Discrete Subgroups Isomorphic to Lattices in Lie Groups

1976 ◽  
Vol 98 (4) ◽  
pp. 853 ◽  
Author(s):  
Gopal Prasad
Keyword(s):  
Lie Groups ◽  
Discrete Subgroups

SU(2)k MODULAR-INVARIANT PARTITION FUNCTIONS FROM ORBIFOLDS

1991 ◽  
Vol 06 (26) ◽  
pp. 4763-4767 ◽  
Author(s):  
F. ARDALAN ◽  
H. ARFAEI ◽  
S. ROUHANI
Keyword(s):  
Conformal Group ◽  
Partition Functions ◽  
Discrete Subgroups ◽  
Modular Invariant ◽  
Orbifold Construction

We present a method which generates the modular-invariant partition functions of the ADE series of SU(2)k. Dividing the diagonal theory by discrete subgroups of the conformal group, we construct all the modular-invariant partition functions, thus proving that orbifold construction generates all the partition functions of SU(2)k.

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