Link Homotopy in S^n x R^{m-n} and Higher Order mu-invariants
Algebraic Topology
2007-05-23 v1 Geometric Topology
Abstract
Given a suitable link map f into a manifold M, we constructed, in [10], link homotopy invariants kappa(f) and mu(f). In the present paper we study the case M=S^n x R^{m - n} in detail. Here mu(f) turns out to be the starting term of a whole sequence mu^(s)(f), s = 0, 1, ..., of higher mu-invariants which together capture all the information contained in kappa(f). We discuss the geometric significance of these new invariants. In several instances we obtain complete classification results. A central ingredient of our approach is the homotopy theory of wedges of spheres.
Cite
@article{arxiv.math/0606034,
title = {Link Homotopy in S^n x R^{m-n} and Higher Order mu-invariants},
author = {Ulrich Koschorke},
journal= {arXiv preprint arXiv:math/0606034},
year = {2007}
}