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The following book has a wealth of material on this topic:

The geometry and topology of Coxeter groups by Michael Davis.

By way of example, here is one result from the book:

Theorem 8.7.1 Let $(W,S)$ be a Coxeter System:

 
  1. $W$ is one-ended if and only $H_c^1(\Sigma)=0$.

    $W$ is one-ended if and only $H_c^1(\Sigma)=0$.

  1. $W$ has two ends if and only $H_c^1(\Sigma)\cong\mathbb{Z}$.
  1. $W$ has two ends if and only $H_c^1(\Sigma)\cong\mathbb{Z}$.

  2. $W$ has infinitely many ends if and only if $H_c^1(\Sigma)$ has infinite rank.

    $W$ has infinitely many ends if and only if $H_c^1(\Sigma)$ has infinite rank.

Here $\Sigma$ is the cell complex associated to $(W,S)$. I have an e-copy of the book - email me if you want a copy.

The following book has a wealth of material on this topic:

The geometry and topology of Coxeter groups by Michael Davis.

By way of example, here is one result from the book:

Theorem 8.7.1 Let $(W,S)$ be a Coxeter System:

 
  1. $W$ is one-ended if and only $H_c^1(\Sigma)=0$.
  1. $W$ has two ends if and only $H_c^1(\Sigma)\cong\mathbb{Z}$.
  1. $W$ has infinitely many ends if and only if $H_c^1(\Sigma)$ has infinite rank.

Here $\Sigma$ is the cell complex associated to $(W,S)$. I have an e-copy of the book - email me if you want a copy.

The following book has a wealth of material on this topic:

The geometry and topology of Coxeter groups by Michael Davis.

By way of example, here is one result from the book:

Theorem 8.7.1 Let $(W,S)$ be a Coxeter System:

  1. $W$ is one-ended if and only $H_c^1(\Sigma)=0$.

  2. $W$ has two ends if and only $H_c^1(\Sigma)\cong\mathbb{Z}$.

  3. $W$ has infinitely many ends if and only if $H_c^1(\Sigma)$ has infinite rank.

Here $\Sigma$ is the cell complex associated to $(W,S)$. I have an e-copy of the book - email me if you want a copy.

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Nick Gill
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The following book has a wealth of material on this topic:

The geometry and topology of Coxeter groups by Michael Davis.

By way of example, here is one result from the book:

Theorem 8.7.1 Let $(W,S)$ be a Coxeter System:

  1. $W$ is one-ended if and only $H_c^1(\Sigma)=0$.
  1. $W$ has two ends if and only $H_c^1(\Sigma)\cong\mathbb{Z}$.
  1. $W$ has infinitely many ends if and only if $H_c^1(\Sigma)$ has infinite rank.

Here $\Sigma$ is the cell complex associated to $(W,S)$. I have an e-copy of the book - email me if you want a copy.