Aspherical manifolds that cannot be triangulated
نویسندگان
چکیده
Although Kirby and Siebenmann [13] showed that there are manifolds which do not admit PL structures, the possibility remained that all manifolds could be triangulated. In the late seventies Galewski and Stern [10] constructed a closed 5–manifold M 5 so that every n–manifold, with n 5, can be triangulated if and only if M 5 can be triangulated. Moreover, M 5 admits a triangulation if and only if the Rokhlin – invariant homomorphism, W H 3 ! Z=2, is split. In 2013 Manolescu [14] showed that the –homomorphism does not split. Consequently, there exist Galewski–Stern manifolds M n that are not triangulable for each n 5.
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