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Timeline for Order of a loop around a cone point

Current License: CC BY-SA 4.0

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Mar 8 at 18:34 history became hot network question
Mar 8 at 15:55 vote accept RKS
Mar 8 at 15:18 history edited YCor CC BY-SA 4.0
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Mar 8 at 13:31 history edited HJRW
Added relevant arXiv subject tag
Mar 8 at 13:29 comment added HJRW @Henri: existence of a non-positively curved metric is much weaker than the full strength of uniformisation (which says that each conformal class of metrics contains a constant-curvature representative).
Mar 8 at 13:27 answer added HJRW timeline score: 6
Mar 8 at 13:20 comment added Henri This is correct yes. For instance, you can say that $M$ admits an orbifold metric with non-positive (actually negative if $p>1$) curvature thanks to uniformization. This tells you that $M$ is developable hence the local isotropy groups inject in the fundamental group. I imagine that there is probably a better, direct way to see this though.
Mar 8 at 10:34 history asked RKS CC BY-SA 4.0