Transfer maps for triples of manifolds
type: Item
instance of: scholarly article
title: Transfer maps for triples of manifolds
zbMATH Open document ID: 1128.57032
published in: Mathematical Notes
publication date: 2007-05-21T00:00:00Z
review text: If \(Y^{n-q}\subset X^{n}\) is a codimension \(q\) submanifold with normal bundle \(\xi\) in an \(n\)-manifold \(X\), and \(\partial U_{\xi}\) is the boundary of a tubular neighbourhood of \(Y\) in \(X\) one can define transfer maps of Wall groups \[ \begin{aligned} \text{tr}_{\xi} &: L_{n-q}(\pi_{1}(Y)) \to L_{n}(\pi_{1}(\partial U_{\xi}) \to \pi_{1}(U_{\xi})),\\ \text{tr}'_{\xi} &: L_{n-q}(\pi_{1}(Y)) \to L_{n}(\pi_{1}(\partial U_{\xi})).\end{aligned} \] This paper describes relations between the transfer maps associated to a triple of embeddings \(Z \subset Y\subset X\). This is done by introducing a relative transfer map \[ \text{tr}^{\text{rel}}: L_{n-q}(\pi_{1}(Y \setminus Z) \to \pi_{1}(Y)) \to L_{n} (\pi_{1}(X \setminus Z) \to \pi_{1}(X)) . \]
Mathematics Subject Classification ID: 57R65
Mathematics Subject Classification ID: 55R12
Mathematics Subject Classification ID: 18F25
zbMATH DE Number: 5155464
zbMATH Keywords: Browder-Livesay invariant
zbMATH Keywords: Wu class
zbMATH Keywords: transfer map
zbMATH Keywords: surgery obstruction
zbMATH Keywords: Wall groups
zbMATH Keywords: normal map
author: Yuri V. Muranov
author: Rolando Jiménez
reviewed by: Jonathan Hodgson
MaRDI profile type: Publication
full work available at URL: s11006-006-0043-5
OpenAlex ID: W2077075288
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DOI: 10.1007/S11006-006-0043-5
description: scientific article; zbMATH DE number 5155464