2020-08-04T21:07:26Zhttps://repository.dl.itc.u-tokyo.ac.jp/?action=repository_oaipmhoai:repository.dl.itc.u-tokyo.ac.jp:000400432020-07-10T06:57:17Z00312:06865:06909:0691500009:00504:06868:06911:06916
An Invariant of Embeddings of 3-Manifolds in 6-Manifolds and Milnor's Triple Linking Numberenghttp://hdl.handle.net/2261/52706Departmental Bulletin PaperMoriyama, TetsuhiroWe 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 Tokyo1821932372011-12-0913405705AA11021653415https://repository.dl.itc.u-tokyo.ac.jp/?action=repository_action_common_download&item_id=40043&item_no=1&attribute_id=19&file_no=1Graduate School of Mathematical Sciences, The University of Tokyo2017-06-14