Relative Hauptvermutung for Neighborhoods of 1-flat Submanifolds with Codimension Two
نویسنده
چکیده
1. Recently Kirby and Siebenmann have given general solutions of Hauptvermutung [5] and relative Hauptvermutung for neighborhoods of locally flat submanifolds [ó]. In this note we announce some results about relative Hauptvermutung for neighborhoods of 1-flat submanifolds with codimension two (compare [ l l ] and [3]). We shall say that manifold pairs (Q, M) and (Q', M') are topologically micro-equivalent, if there are open neighborhoods U, TJ' of M, M' in Q, Q' and a homeomorphism h: (U, M)->(U', M'), called a topological micro-equivalence between (Q, M) and ((?', M'). We shall say that PL manifold pairs (Q, M) and (Q', M') are PL micro-equivalent, if there are open neighborhoods V, V of M, M' in Q, Q' and a PL homeomorphism g: (V, M)—>(V', M'), called a PL micro-equivalence between «?, M) and «?', M'). We shall prove the following
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