Derivatives of the identity and generalizations of Milnor's invariants

Details Derivatives of the identity and generalizations of Milnor's invariants Derivatives of the identity and generalizations of Milnor's invariants

2009-09-16

arxiv.org/abs/0909.3074v2

Mathematics

Algebraic Topology

25 pages, accepted for publication by the Journal of Topology

Scientific paper

We synthesize work of U. Koschorke on link maps and work of B. Johnson on the derivatives of the identity functor in homotopy theory. The result can be viewed in two ways: (1) As a generalization of Koschorke's "higher Hopf invariants", which themselves can be viewed as a generalization of Milnor's invariants of link maps in Euclidean space; and (2) As a stable range description, in terms of bordism, of the cross effects of the identity functor in homotopy theory evaluated at spheres. We also show how our generalized Milnor invariants fit into the framework of a multivariable manifold calculus of functors, as developed by the author and Voli\'{c}, which is itself a generalization of the single variable version due to Weiss and Goodwillie.

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