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Let X and Y be oriented topological manifolds of dimension n + 2, and let Kand J be connected, locally-flat, oriented, n-dimensional submanifolds of X andY. We show that up to orientation preserving homeomorphism there is awell-defined connected sum K # J in X # Y. For n = 1, the proof is classical,relying on results of Rado and Moise. For dimensions n = 3 and n > 5, resultsof Edwards-Kirby, Kirby, and Kirby-Siebenmann concerning higher dimensionaltopological manifolds are required. For n = 2, 4, and 5, Freedman and Quinn'swork on topological four-manifolds is needed. The truth of the correspondingstatement for higher codimension seems to be unknown.

Connected sums of codimension two locally flat submanifolds