How Long to Read Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations

How Long Does it Take to Read Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations?

It takes the average reader 1 hour and 52 minutes to read Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations by Greg Hjorth

Assuming a reading speed of 250 words per minute. Learn more

Description

This memoir is both a contribution to the theory of Borel equivalence relations, considered up to Borel reducibility, and measure preserving group actions considered up to orbit equivalence. Here $E$ is said to be Borel reducible to $F$ if there is a Borel function $f$ with $x E y$ if and only if $f(x) F f(y)$. Moreover, $E$ is orbit equivalent to $F$ if the respective measure spaces equipped with the extra structure provided by the equivalence relations are almost everywhere isomorphic. We consider product groups acting ergodically and by measure preserving transformations on standard Borel probability spaces.In general terms, the basic parts of the monograph show that if the groups involved have a suitable notion of 'boundary' (we make this precise with the definition of near hyperbolic), then one orbit equivalence relation can only be Borel reduced to another if there is some kind of algebraic resemblance between the product groups and coupling of the action. This also has consequence for orbit equivalence. In the case that the original equivalence relations do not have non-trivial almost invariant sets, the techniques lead to relative ergodicity results. An equivalence relation $E$ is said to be relatively ergodic to $F$ if any $f$ with $xEy \Rightarrow f(x) F f(y)$ has $[f(x)]_F$ constant almost everywhere.This underlying collection of lemmas and structural theorems is employed in a number of different ways. In the later parts of the paper, we give applications of the theory to specific cases of product groups. In particular, we catalog the actions of products of the free group and obtain additional rigidity theorems and relative ergodicity results in this context. There is a rather long series of appendices, whose primary goal is to give the reader a comprehensive account of the basic techniques. But included here are also some new results. For instance, we show that the Furstenberg-Zimmer lemma on cocycles from amenable groups fails with respect to Baire category, and use this to answer a question of Weiss. We also present a different proof that $F_2$ has the Haagerup approximation property.

How long is Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations?

Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations by Greg Hjorth is 109 pages long, and a total of 28,231 words.

This makes it 37% the length of the average book. It also has 35% more words than the average book.

How Long Does it Take to Read Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 34 minutes to read Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations aloud.

What Reading Level is Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations?

Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations?

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