Abstract
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 language | English |
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Pages (from-to) | 2443-2460 |
Number of pages | 18 |
Journal | COMPOSITIO MATHEMATICA |
Early online date | 25 Oct 2016 |
DOIs | |
Publication status | Published - Dec 2016 |
Keywords
- Alexandrov geometry
- CAT[0] spaces
- hyperplane arrangements
- polyhedral spaces