Homotopy Lie algebras and submanifolds
type: Item
instance of: scholarly article
title: Homotopy Lie algebras and submanifolds
zbMATH Open document ID: 0812.57021
DOI: 10.1016/0022-4049(94)90144-9
author: Ştefan Papadima
published in: Journal of Pure and Applied Algebra
publication date: 1995-05-21T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 500574
zbMATH Keywords: Poincaré transfer
zbMATH Keywords: Thom space
zbMATH Keywords: embedding in an elliptic formal manifold
zbMATH Keywords: rational homotopy Lie algebra
zbMATH Keywords: submanifolds
zbMATH Keywords: normal structure group
zbMATH Keywords: normal characteristic classes
zbMATH Keywords: free graded Lie algebra
Wikidata QID: Q115364398
reviewed by: Yves Félix
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90144-9
OpenAlex ID: W2058164759
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description: scientific article; zbMATH DE number 500574