The Seifert-van Kampen theorem and generalized free products of S-algebras

DC FieldValueLanguage
dc.contributor.authorSchwanzl, R
dc.contributor.authorStaffeldt, R
dc.date.accessioned2021-12-23T16:06:51Z-
dc.date.available2021-12-23T16:06:51Z-
dc.date.issued2002
dc.identifier.issn00029939
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/7581-
dc.description.abstractIn a Seifert-van Kampen situation a path-connected space Z may be written as the union of two open path-connected subspaces X and Y along a common path-connected intersection W. he fundamental group of Z is isomorphic to the colimit of the diagram of fundamental groups of the three subspaces. In case the maps of fundamental groups are all injective, the fundamental group of Z is a classical free product with amalgamation, and the integral group ring of the fundamental group of Z is also a free product with amalgamation in the category of rings. In this case relations among the K theories of the group rings have been studied. Here we describe a generalization and stablization of this algebraic fact, where there are no injectivity hypotheses on the fundamental groups and where we work in the category of S-algebras. Some of the methods we use are classical and familiar, but the passage to S-algebras blends classical and new techniques. Our most important application is a description of the algebraic K-theory of the space Z in terms of the algebraic K-theories of the other three spaces and the algebraic K-theory of spaces Nil-term.
dc.language.isoen
dc.publisherAMER MATHEMATICAL SOC
dc.relation.ispartofPROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
dc.subjectMathematics
dc.subjectMathematics, Applied
dc.titleThe Seifert-van Kampen theorem and generalized free products of S-algebras
dc.typejournal article
dc.identifier.doi10.1090/S0002-9939-02-06521-8
dc.identifier.isiISI:000176744300010
dc.description.volume130
dc.description.issue11
dc.description.startpage3193
dc.description.endpage3208
dc.publisher.place201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA
dcterms.isPartOf.abbreviationProc. Amer. Math. Soc.
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