Ramification conjecture and Hirzebruch’s property of line arrangements

D. Panov*, A. Petrunin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
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The ramification of a polyhedral space is defined as the metric completion of the universal cover of its regular locus. We consider mainly polyhedral spaces of two origins: quotients of Euclidean space by a discrete group of isometries and polyhedral metrics on (Formula presented.) with singularities at a collection of complex lines. In the former case we conjecture that quotient spaces always have a (Formula presented.) ramification and prove this in several cases. In the latter case we prove that the ramification is (Formula presented.) if the metric on (Formula presented.) is non-negatively curved. We deduce that complex line arrangements in (Formula presented.) studied by Hirzebruch have aspherical complement.

Original languageEnglish
Pages (from-to)2443-2460
Number of pages18
Early online date25 Oct 2016
Publication statusPublished - Dec 2016


  • Alexandrov geometry
  • CAT[0] spaces
  • hyperplane arrangements
  • polyhedral spaces

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