, Volume 97, Issue 1, pp 195-207

The algebraic characterization of the exteriors of certain 2-knots

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We study 2-knots with virtually solvable group by applying recent work of Freedman to the 4-manifolds obtained by surgery on such knots. In particular we show that “Gluck reconstruction” is the only ambiguity in recovering the Cappell-Shaneson knots (as TOP locally flat knots) from their groups alone.