scholarly journals A rigidity theorem for holomorphic generators on the Hilbert ball

2008 ◽  
Vol 136 (12) ◽  
pp. 4313-4320 ◽  
Author(s):  
Mark Elin ◽  
Marina Levenshtein ◽  
Simeon Reich ◽  
David Shoikhet
Keyword(s):  
Rigidity Theorem ◽  
Hilbert Ball

scholarly journals Profinite rigidity for twisted Alexander polynomials

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jun Ueki
Keyword(s):  
Rigidity Theorem ◽  
Homology Groups ◽  
Alexander Polynomials ◽  
Twisted Homology ◽  
Hyperbolic Volumes

AbstractWe formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the twisted homology groups in a {{\mathbb{Z}}}-cover of a 3-manifold with use of Mahler measures. We examine several examples associated to Riley’s parabolic representations of two-bridge knot groups and give a remark on hyperbolic volumes.

Some Inequalities for the Horosphere Function and Hyperbolically Nonexpansive Mappings on the Hilbert Ball

2014 ◽  
Vol 201 (5) ◽  
pp. 595-613
Author(s):  
M. Elin ◽  
M. Levenshtein ◽  
S. Reich ◽  
D. Shoikhet
Keyword(s):  
Nonexpansive Mappings ◽  
Hilbert Ball

scholarly journals Schreir graphs: Transitivity and coverings

2016 ◽  
Vol 26 (01) ◽  
pp. 69-93 ◽  
Author(s):  
Paul-Henry Leemann
Keyword(s):  
Hyperbolic Manifolds ◽  
Rigidity Theorem ◽  
Partial Answer ◽  
Schreier Graphs

We give a characterization of isomorphisms between Schreier graphs in terms of the groups, subgroups and generating systems. This characterization may be thought as a graph analog of Mostow’s rigidity theorem for hyperbolic manifolds. This allows us to give a transitivity criterion for Schreier graphs. Finally, we show that Tarski monsters satisfy a strong simplicity criterion. This gives a partial answer to a question of Benjamini and Duminil-Copin.

scholarly journals Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Yasunori Kimura
Keyword(s):  
Projection Method ◽  
Convergence Theorem ◽  
Iterative Scheme ◽  
Equivalent Condition ◽  
Set Convergence ◽  
Hadamard Space ◽  
Shrinking Projection Method ◽  
Metric Projections ◽  
Hilbert Ball

We propose a new concept of set convergence in a Hadamard space and obtain its equivalent condition by using the notion of metric projections. Applying this result, we also prove a convergence theorem for an iterative scheme by the shrinking projection method in a real Hilbert ball.

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