scholarly journals Weak equivalence to Bernoulli shifts for some algebraic actions

2019 ◽  
Vol 147 (5) ◽  
pp. 2021-2032
Author(s):  
Ben Hayes
Keyword(s):  
Weak Equivalence ◽  
Bernoulli Shifts ◽  
Algebraic Actions

scholarly journals Harmonic models and Bernoullicity

2021 ◽  
Vol 157 (10) ◽  
pp. 2160-2198
Author(s):  
Ben Hayes
Keyword(s):  
Orderable Group ◽  
Bernoulli Shifts ◽  
Algebraic Actions ◽  
Bernoulli Partition

We give many examples of algebraic actions which are factors of Bernoulli shifts. These include certain harmonic models over left-orderable groups of large enough growth, as well as algebraic actions associated to certain lopsided elements in any left-orderable group. For many of our examples, the acting group is amenable so these actions are Bernoulli (and not just a factor of a Bernoulli), but there is no obvious Bernoulli partition.

On equivariant disconnected rational homotopy theory

2010 ◽  
Vol 17 (2) ◽  
pp. 229-240
Author(s):  
Marek Golasiński
Keyword(s):  
Homotopy Theory ◽  
Weak Equivalence ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Hamiltonian Group ◽  
Simplicial Set ◽  
De Rham

Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

scholarly journals Testing the Weak Equivalence Principle Using Optical and Near-infrared Crab Pulses

2018 ◽  
Vol 861 (1) ◽  
pp. 66 ◽  
Author(s):  
Calvin Leung ◽  
Beili Hu ◽  
Sophia Harris ◽  
Amy Brown ◽  
Jason Gallicchio ◽  
...  
Keyword(s):  
Equivalence Principle ◽  
Near Infrared ◽  
Weak Equivalence ◽  
Weak Equivalence Principle

Invariants of weak equivalence in primitive matrices

2000 ◽  
Vol 20 (2) ◽  
pp. 611-626 ◽  
Author(s):  
RICHARD SWANSON ◽  
HANS VOLKMER
Keyword(s):  
Inverse Limit ◽  
Direct Application ◽  
Topological Classification ◽  
Weak Equivalence ◽  
Transition Matrices ◽  
Inverse Limit Spaces ◽  
Positive Dimension ◽  
One Dimensional ◽  
Dimension Group

Weak equivalence of primitive matrices is a known invariant arising naturally from the study of inverse limit spaces. Several new invariants for weak equivalence are described. It is proved that a positive dimension group isomorphism is a complete invariant for weak equivalence. For the transition matrices corresponding to periodic kneading sequences, the discriminant is proved to be an invariant when the characteristic polynomial is irreducible. The results have direct application to the topological classification of one-dimensional inverse limit spaces.

Cantor Sets, Bernoulli Shifts and Linear Dynamics

2014 ◽  
pp. 195-207 ◽  
Author(s):  
Salud Bartoll ◽  
Félix Martínez-Giménez ◽  
Marina Murillo-Arcila ◽  
Alfredo Peris
Keyword(s):  
Cantor Sets ◽  
Linear Dynamics ◽  
Bernoulli Shifts

scholarly journals Spaces which Invert Weak Homotopy Equivalences

2018 ◽  
Vol 62 (2) ◽  
pp. 553-558
Author(s):  
Jonathan Ariel Barmak
Keyword(s):  
Empty Space ◽  
Weak Equivalence ◽  
Homotopy Equivalence ◽  
Homotopy Classes ◽  
Cw Complex ◽  
Cw Complexes ◽  
Weak Homotopy ◽  
Weak Homotopy Equivalence

AbstractIt is well known that if X is a CW-complex, then for every weak homotopy equivalence f : A → B, the map f* : [X, A] → [X, B] induced in homotopy classes is a bijection. In fact, up to homotopy equivalence, only CW-complexes have that property. Now, for which spaces X is f* : [B, X] → [A, X] a bijection for every weak equivalence f? This question was considered by J. Strom and T. Goodwillie. In this note we prove that a non-empty space inverts weak equivalences if and only if it is contractible.

scholarly journals Tests of weak equivalence principle with the gravitational wave signals in the LIGO–Virgo catalogue GWTC-1

2020 ◽  
Vol 499 (1) ◽  
pp. L53-L57
Author(s):  
Shu-Cheng Yang ◽  
Wen-Biao Han ◽  
Gang Wang
Keyword(s):  
Gravitational Wave ◽  
Equivalence Principle ◽  
Arrival Time ◽  
Gamma Ray ◽  
Weak Equivalence ◽  
Radio Bursts ◽  
Weak Equivalence Principle ◽  
Massive Galaxies ◽  
Binary Black Hole ◽  
Gravitational Theories

ABSTRACT The weak equivalence principle (WEP) is the cornerstone of gravitational theories. At the local scale, WEP has been tested to high accuracy by various experiments. On the intergalactic distance scale, WEP could be tested by comparing the arrival time of different messengers emitted from the same source. The gravitational time delay caused by massive galaxies is proportional to γ + 1, where the parameter γ is unity in general relativity. The values of γ for different massless particles should be different if WEP is violated, i.e. Δγ is used to indicate the deviation from WEP. So far, |Δγ| has been constrained with gamma-ray bursts, fast radio bursts, etc. Here, we report a new constraint of |Δγ| by using the gravitational wave data of binary black hole coalescences in the LIGO–Virgo catalogue GWTC-1. The best constraints imply that |Δγ| ≲ 10−15 at 90 per cent confidence level.

Precision tests of Einstein's Weak Equivalence Principle for antimatter

2000 ◽  
Vol 25 (6) ◽  
pp. 1245-1249 ◽  
Author(s):  
F.M. Huber ◽  
R.A. Lewis ◽  
E.W. Messerschmid ◽  
G.A. Smith
Keyword(s):  
Equivalence Principle ◽  
Weak Equivalence ◽  
Weak Equivalence Principle
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