http://swrc.ontoware.org/ontology#UnrefereedArticle
An Invariant of Embeddings of 3-Manifolds in 6-Manifolds and Milnor's Triple Linking Number
en
Moriyama Tetsuhiro
We give a simple axiomatic definition of a rational-valued invariant σ(W, V, e) of triples (W, V, e), where W ⊃ V are smooth oriented closed manifolds of dimensions 6 and 3, and e is a second rational cohomology class of the complement W \ V satisfying a certain condition. The definition is stated in terms of cobordisms of such triples and the signature of 4-manifolds. When W = S6 and V is a smoothly embedded 3-sphere, and when e/2 is the Poincaré dual of a Seifert surface of V, the invariant coincides with -8 times Haefliger's embedding invariant of (S6, V). Our definition recovers a more general invariant due to Takase, and contains a new definition for Milnor's triple linking number of algebraically split 3-component links in R3 that is close to the one given by the perturbative series expansion of the Chern-Simons theory of links in R3.
Journal of mathematical sciences, the University of Tokyo
18
2
193-237
2011-12-09
13405705
AA11021653
415
Graduate School of Mathematical Sciences, The University of Tokyo