Geometry of free products
type: Item
instance of: scholarly article
title: Geometry of free products
zbMATH Open document ID: 0584.20016
DOI: 10.1007/BF01160479
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173809
review text: The rank of the free factor of a subgroup \(\Phi\) of a free product \(\Gamma =\prod^{*}_{i\in I}\Gamma_ i\) given by Kurosh's theorem is a well-defined invariant of \(\Phi\) as a subgroup of \(\Gamma\) and it has some analogies with the genus and the number of cusps of a subgroup of a fuchsian group. We explain these analogies by means of the diagrams and their thickenings introduced in an earlier paper and give extensions of a number of results by Greenberg, Millington, Newman, Rosenberger, Zieschang....
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 30F35
zbMATH DE Number: 3935297
zbMATH Keywords: Kurosh subgroup theorem
zbMATH Keywords: rank
zbMATH Keywords: free factor
zbMATH Keywords: free product
zbMATH Keywords: genus
zbMATH Keywords: number of cusps
zbMATH Keywords: subgroup of a fuchsian group
zbMATH Keywords: diagrams
author: Ravindra S. Kulkarni
MaRDI profile type: Publication
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OpenAlex ID: W2025330683
description: scientific article; zbMATH DE number 3935297