Freedman's conjecture on surgery for free groups

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Let MM be a topological 44-manifold, let ∨3S1{\vee}^3 S^1 denote the wedge of three circles, and let S0(Wh(Bor)){\mathcal S}^0(Wh(Bor)) denote the zero-framed surgery on the Whitehead double of the Borromean rings. Freedman's conjecture. There does not exist a topological 44-manifold MM homotopy equivalent to ∨3S1{\vee}^3 S^1 whose boundary is homeomorphic to S0(Wh(Bor)){\mathcal S}^0(Wh(Bor)). This conjecture concerns the failure of topological surgery for free fundamental groups, in contrast with the known surgery results for simply connected and other good groups; its resolution is not specified in the supplied text.

References

Primary source

Vyacheslav Krushkal, “Link groups and the A-B slice problem”, arXiv:math/0602105 (2008).

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