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Piecewise linear embeddings and isotopies

1966
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Bulletin of the American Mathematical Society
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Let M and Q be PL manifolds of dimensions m and q respectively, M being compact. Let dM and dQ be their boundaries, possibly empty. If ƒ : M->Q is any continuous mapping, ir f (ƒ) will denote the relative homotopy group of the pair (C/, AT), Cf being the mapping cylinder of ƒ : M-+Q. THE EMBEDDING THEOREM. Let ƒ: M-*Q be a mapping such that f~l(dQ) =dM, and the restriction f \d M is a PL embedding. If q -'M è 3, *>(ƒ) = 0 for r ^ 2m -q + 1, TT r (M) = 0 forrS3m~2q+2 9 then f is homotopic,

doi:10.1090/s0002-9904-1966-11532-x
fatcat:wfh7ub4lajgq3ipxas4t34nwmi