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      Homotopy properties of knots in prime manifolds

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          Abstract

          We define homotopy-theoretic invariants of knots in prime 3-manifolds. Fix a knot J in a prime 3-manifold M. Call a knot K in M concordant to J if it cobounds a properly embedded annulus with J in MxI, and call K J-characteristic if there is a degree-one map f:M --> M throwing K onto J and mapping M-K to M-J. These invariants are invariants of concordance and of J-characteristicness when f induces the identity on the fundamental group of M, and may be viewed as extensions of Milnor's invariants. We do not require the knots considered here to be rationally null-homologous or framed.

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          Homology and central series of groups

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            Knot concordance, Whitney towers and L2-signatures

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              Homotopy invariants of links

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                Author and article information

                Journal
                31 October 2011
                Article
                1110.6903
                bb5932c4-61e6-46e5-bfa7-8a5d91658472

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.GT math.AT

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