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 CP2 with singularities at a collection of complex lines. In the former case we conjecture that quotient spaces always have a CAT[0] ramification and prove this in several cases. In the latter case we prove that the ramification is CAT[0] if the metric on CP2 is non-negatively curved. We deduce that complex line arrangements in CP2 studied by Hirzebruch have aspherical complement.
Original language | English (US) |
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Pages (from-to) | 2443-2460 |
Number of pages | 18 |
Journal | Compositio Mathematica |
Volume | 152 |
Issue number | 12 |
DOIs | |
State | Published - Dec 1 2016 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory