Quasi‐isometry invariance of group splittings over coarse Poincaré duality groups

We show that if G is a group of type F P n + 1 Z 2 that is coarsely separated into three essential, coarse disjoint, coarse complementary components by a coarse P D n Z 2 space W , then W is at finite Hausdorff distance from a subgroup H of G ; moreover, G splits over a subgroup commensurable to a s...