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Twisted Blanchfield pairings and decompositions of 3-manifolds

Friedl, Stefan ; Leidy, Constance ; Nagel, Matthias ; Powell, Mark


We prove a decomposition formula for twisted Blanchfield pairings of 3-manifokls. As an application we show that the twisted Blanchfield pairing of a 3-manifold obtained from a 3-manifold Y with a representation ?: Z[pi(1)(Y)]-> R, infected by a knot J along a curve eta with ?(eta)not equal 1, splits orthogonally as the sum of the twisted Blanchfield pairing of Y and the ordinary Blanchfield pairing of the knot J, with the latter tensored up from Z[t,t (-1)] to 11.

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