The higher dimensional Poincaré conjecture claims that any closed n-dimensional manifold which is homotopy equivalent to the n-sphere must be the n-sphere.
Ang mas mataas na sukat Poincaré haka-haka na pag-angkin ng anumang sarado n-dimensional sari-sari na kung saan ay homotopy katumbas sa n-abot ay dapat na ang n-abot.