Construction of an infinitely generated group that is not a free product of surface groups and abelian groups, but which acts freely on an ℝ-tree

DOI10.1017/S0308210500012877zbMath0913.20028MaRDI QIDQ3840015

Andreas Zastrow

Publication date: 8 June 1999

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

finitely generated groupsfree productsfundamental groupssurface groups\(\mathbb{R}\)-treesHawaiian Earringsinverse limits of finitely generated free groups

Mathematics Subject Classification ID

Geometric group theory (20F65) Fundamental group, presentations, free differential calculus (57M05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Group actions on manifolds and cell complexes in low dimensions (57M60) Groups acting on trees (20E08)

Related Items (10)

The word problem for some uncountable groups given by countable words ⋮ On semilocally simply connected spaces ⋮ An uncountable homology group, where each element is an infinite product of commutators ⋮ ACTIONS, LENGTH FUNCTIONS, AND NON-ARCHIMEDEAN WORDS ⋮ Covering \(\mathbb R\)-trees, \(\mathbb R\)-free groups, and dendrites ⋮ Atomic property of the fundamental groups of the Hawaiian earring and wild locally path-connected spaces ⋮ On the fundamental group of the Sierpiński-gasket ⋮ The non-Abelian Specker-group is free ⋮ Algebraic topology of Peano continua ⋮ Free and non-free subgroups of the fundamental group of the Hawaiian earrings.

Cites Work

• Pseudogroups of isometries of \(\mathbb{R}\) and Rips' theorem on free actions on \(\mathbb{R}\)-trees
• Stable actions of groups on real trees
• Equivalence Classes of Length Functions on Groups
• Infinite Products of Semi-Groups and Local Connectivity
• THE FUNDAMENTAL GROUP OF THE HAWAIIAN EARRING IS NOT FREE
• Complete Trees for Groups with a Real-Valued Length Function
• A Van Kampen Theorem for Weak Joins
• Group Actions On R-Trees
• Abstract length functions in groups
• Length Functions in Groups.
• THE FUNDAMENTAL GROUP OF TWO SPACES WITH A COMMON POINT

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