On Brunnian-type links and the link invariants given by homotopy groups of spheres

Details On Brunnian-type links and the link invariants given by homotopy groups of spheres On Brunnian-type links and the link invariants given by homotopy groups of spheres

2009-09-27

arxiv.org/abs/0909.4973v3

Mathematics

Algebraic Topology

36 pages in this version after adding some examples of links labeled by homotopy group elements and the remarks how to constru

Scientific paper

We introduce the (general) homotopy groups of spheres as link invariants for Brunnian-type links through the investigations on the intersection subgroup of the normal closures of the meridians of strongly nonsplittable links. The homotopy groups measure the difference between the intersection subgroup and symmetric commutator subgroup of the normal closures of the meridians and give the invariants of the links obtained in this way. Moreover the higher homotopy-group invariants can produce some links that could not be detected by the Milnor invariants. Furthermore all homotopy groups of spheres can be obtained from the geometric Massey products on links.

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