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Mar 14, 2015 at 23:32 comment added YCor You need at least one example for which you know that the free product is $CAT(-1)$; it's OK for the free product of a surface group with $\mathbf{Z}$.
Mar 14, 2015 at 17:19 comment added Anton Petrunin word hyperbolic groups are not exactly CAT(-1). (But there are many examples.)
Mar 14, 2015 at 17:03 history answered Igor Rivin CC BY-SA 3.0