Cobordism of manifolds with strong almost tangent structures
type: Item
instance of: scholarly article
title: Cobordism of manifolds with strong almost tangent structures
zbMATH Open document ID: 0552.57012
author: Robert Goggins
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: This paper studies the possible cobordism classes for a closed manifold \(M^ n\) whose tangent bundle has the form \(r\xi\) \(\oplus \eta\). In differential geometry this is called an almost tangent structure of order r-1. Typical results say that \(M^{4k+3}\) with \(\tau =4k\xi^ 1\oplus \eta^ 3\) bounds and that there are manifolds of dimension \(2^ p(2q+1)-1\), \(p\geq 2\), \(q\geq 1\) which are indecomposable in unoriented cobordism for which \(\tau =(2^{p+1}q-1)\xi^ 1+\eta\).
Mathematics Subject Classification ID: 57R75
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 3879742
zbMATH Keywords: cobordism classes
zbMATH Keywords: almost tangent structure of order r-1
MaRDI profile type: Publication
full work available at URL: pjm.1984.115.361
OpenAlex ID: W2011175655
DOI: 10.2140/PJM.1984.115.361
description: scientific article; zbMATH DE number 3879742