Triangulating nonsimply connected manifolds
John Hollingsworth · Bulletin of the American Mathematical Society · 1969
THEOREM.Let M n be a compact topological manifold with boundary iV n "~1, with fundamental group satisfying condition S.(a) If H A (M; Z 2 ) =H Z (N; Z 2 ) = 0, and n è 6, M admits a PL manu fold structure.(b) If N already has a PL structure, H A (M; Z 2 )=*IP(N; Z 2 )=0 and n*z 5, then M admits a PL manifold structure agreeing with the given one on the boundary.