arXiv:0911.3173 Abstract | arXiv Analytics

arXiv:0911.3173 [math.GR]Abstract References Reviews Resources

JSJ decompositions: definitions, existence, uniqueness. I: The JSJ deformation space

Published 2009-11-16, updated 2016-03-25Version 3

This paper and its companion arXiv:1002.4564 have been replaced by arXiv:1602.05139. We give a general simple definition of JSJ decompositions by means of a universal maximality property. The JSJ decomposition should not be viewed as a tree (which is not uniquely defined) but as a canonical deformation space of trees. We prove that JSJ decompositions of finitely presented groups always exist, without any assumption on edge groups. Many examples are given.

Comments: This paper and its companion arXiv:1002.4564 have been replaced by arXiv:1602.05139

Categories: math.GR, math.GT

Subjects: 20E08, 20E34, 20F65, 57M07, 20E06

Keywords: jsj decomposition, jsj deformation space, uniqueness, general simple definition, universal maximality property

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