Classification of homotopy Dold manifolds
type: Item
instance of: scholarly article
title: Classification of homotopy Dold manifolds
zbMATH Open document ID: 1039.57013
author: Himadri Kumar Mukerjee
published in: The New York Journal of Mathematics
publication date: 2004-01-19T00:00:00Z
full work available at URL: https://eudml.org/doc/123623
full work available at URL: 9-14nf.htm
review text: For \(r,s > 1\), the Dold manifold \(P(r,s)\) is a quotient of \(S^r \times \mathbb{C}P^s\) obtained by identifying \((x,y)\sim (x',y')\) iff \(x'=-x\) and \(y'=\bar{y}\). Thus, \(P(r,s)\) fibers over \(\mathbb{R}P^r\) with fiber \(\mathbb{C}P^s\). In this paper all manifolds homotopy equivalent to \(P(r,s)\) are classified in the piecewise linear and topological categories from the point of view of surgery theory. That is, the groups and maps in the surgery exact sequence are calculated. Moreover, the same is done for products of \(P(r,s)\) with disks of all dimensions. Partial results are obtained in the smooth category.
reviewed by: Bruce Hughes
Mathematics Subject Classification ID: 57N65
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 57R19
Mathematics Subject Classification ID: 57R67
Mathematics Subject Classification ID: 57R65
Mathematics Subject Classification ID: 19J25
zbMATH DE Number: 2028908
zbMATH Keywords: surgery theory
zbMATH Keywords: surgery obstruction
zbMATH Keywords: normal invariant
zbMATH Keywords: Browder-Livesay invariant
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2028908