Large facing tuples and a strengthened sector lemma
Large facing tuples and a strengthened sector lemma
We prove a strengthened sector lemma for irreducible, finite-dimensional, locally finite, essential, cocompact CAT(0) cube complexes under the additional hypothesis that the complex is \emph{hyperplane-essential}; we prove that every quarterspace contains a halfspace. In aid of this, we present simplified proofs of known results about loxodromic isometries of the contact …