Homotopy Lie algebras and submanifolds
Let \(V\) be a closed oriented connected manifold and \(G\) be a closed connected subgroup of \(\text{SO}(q)\). The author explores relationship between the structure of the Lie algebra \(\pi_ *(\Omega V) \otimes \Omega\) and the set of closed oriented codimension-\(q\) submanifolds \(W\) of \(V\) having \(G\) as normal structure group. He gives a condition on the normal characteristic classes of \(W\) that implies that \(\pi_ *(\Omega V) \otimes Q\) contains a free graded Lie algebra on two generators. As a corollary he obtains new restrictions on the homological behaviour of the embedding of a given \(W\) in a given elliptic formal manifold.
embedding in an elliptic formal manifold
scientific article; zbMATH DE number 500574
scientific article