How Long to Read Connectivity Properties of Group Actions on Non-Positively Curved Spaces

How Long Does it Take to Read Connectivity Properties of Group Actions on Non-Positively Curved Spaces?

It takes the average reader 1 hour and 23 minutes to read Connectivity Properties of Group Actions on Non-Positively Curved Spaces by Robert Bieri

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

Description

Generalizing the Bieri-Neumann-Strebel-Renz Invariants, this Memoir presents the foundations of a theory of (not necessarily discrete) actions $\rho$ of a (suitable) group $G$ by isometries on a proper CAT(0) space $M$. The passage from groups $G$ to group actions $\rho$ implies the introduction of 'Sigma invariants' $\Sigma^k(\rho)$ to replace the previous $\Sigma^k(G)$ introduced by those authors. Their theory is now seen as a special case of what is studied here so that readers seeking a detailed treatment of their theory will find it included here as a special case. We define and study 'controlled $k$-connectedness $(CC^k)$' of $\rho$, both over $M$ and over end points $e$ in the 'boundary at infinity' $\partial M$; $\Sigma^k(\rho)$ is by definition the set of all $e$ over which the action is $(k-1)$-connected. A central theorem, the Boundary Criterion, says that $\Sigma^k(\rho) = \partial M$ if and only if $\rho$ is $CC^{k-1}$ over $M$.An Openness Theorem says that $CC^k$ over $M$ is an open condition on the space of isometric actions $\rho$ of $G$ on $M$. Another Openness Theorem says that $\Sigma^k(\rho)$ is an open subset of $\partial M$ with respect to the Tits metric topology. When $\rho(G)$ is a discrete group of isometries the property $CC^{k-1}$ is equivalent to ker$(\rho)$ having the topological finiteness property type '$F_k$'. More generally, if the orbits of the action are discrete, $CC^{k-1}$ is equivalent to the point-stabilizers having type $F_k$. In particular, for $k=2$ we are characterizing finite presentability of kernels and stabilizers. Examples discussed include: locally rigid actions, translation actions on vector spaces (especially those by metabelian groups), actions on trees (including those of $S$-arithmetic groups on Bruhat-Tits trees), and $SL_2$ actions on the hyperbolic plane.

How long is Connectivity Properties of Group Actions on Non-Positively Curved Spaces?

Connectivity Properties of Group Actions on Non-Positively Curved Spaces by Robert Bieri is 83 pages long, and a total of 20,999 words.

This makes it 28% the length of the average book. It also has 26% more words than the average book.

How Long Does it Take to Read Connectivity Properties of Group Actions on Non-Positively Curved Spaces Aloud?

The average oral reading speed is 183 words per minute. This means it takes 1 hour and 54 minutes to read Connectivity Properties of Group Actions on Non-Positively Curved Spaces aloud.

What Reading Level is Connectivity Properties of Group Actions on Non-Positively Curved Spaces?

Connectivity Properties of Group Actions on Non-Positively Curved Spaces 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 Connectivity Properties of Group Actions on Non-Positively Curved Spaces?

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