Homotopy properties of knots in prime manifolds
  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. 
Prudence Heck
math.GT math.AT