Topological types of complex isolated hypersurface singularities
type: Item
instance of: scholarly article
title: Topological types of complex isolated hypersurface singularities
zbMATH Open document ID: 0674.32006
author: Osamu Saeki
published in: Kodai Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: There are four different definitions of topological types of a holomorphic germ which has an isolated critical point at the origin. They are called that ``topologically right equivalent'', ``topologically right-left equivalent'', ``topologically V-equivalent'' and ``link equivalent''. In this paper, the author considers and studies whether those definitions are equivalent or not. By the definitions, the right equivalence implies the right-left equivalence, which in turn implies the V-equivalence. And the link equivalence obviously implies the V-equivalence. Theorem 1. If two holomorphic function germs with isolated critical points at the origin are topologically V-equivalent, then they are link equivalent. Theorem 2. Let f and g be holomorphic function germs with isolated critical points at the origin. Then the following three are equivalent. (a) f and g are topologically right-left equivalent. (b) f and g are topologically V-equivalent. (c) f and g are link equivalent.
Mathematics Subject Classification ID: 32Sxx
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 4103448
zbMATH Keywords: topologically right equivalent
zbMATH Keywords: topologically right-left equivalent
zbMATH Keywords: topologically V-equivalent
zbMATH Keywords: link equivalent
reviewed by: S. Ohyanagi
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138038986
OpenAlex ID: W2033583779
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DOI: 10.2996/KMJ/1138038986
description: scientific article; zbMATH DE number 4103448