The Finite and Infinite Generation of Groups Acting on CAT(0)-cube complexes
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Type
ThesisThesis type
Masters by ResearchAuthor/s
Badre, CarolAbstract
This MPhil thesis explores groups acting on CAT(0)-cube complexes X- in particular, non-uniform lattices Γ ≤ Aut(X). The first section provides a new proof of the classical result that non-uniform tree lattices are not finitely generated. Using the more general setting of essential ...
See moreThis MPhil thesis explores groups acting on CAT(0)-cube complexes X- in particular, non-uniform lattices Γ ≤ Aut(X). The first section provides a new proof of the classical result that non-uniform tree lattices are not finitely generated. Using the more general setting of essential actions studied in detail in Caprace and Sageev’s Rank Rigidity of CAT(0)-cube complexes and Sageev’s early work, the author proves that non-uniform lattices acting on CAT(0)-cube complexes with strict fundamental domain are not finitely generated- generalising the work of Thomas and Wortman in the case of non-uniform lattices of right-angled buildings. The final section is the construction of the quotient and complex of groups of SL2(F2[t, t−1 ]) acting on T3 × T3, the product of Bruhat-Tits trees corresponding to SL2(F2((t))) and SL2(F2((t −1 ))).
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See moreThis MPhil thesis explores groups acting on CAT(0)-cube complexes X- in particular, non-uniform lattices Γ ≤ Aut(X). The first section provides a new proof of the classical result that non-uniform tree lattices are not finitely generated. Using the more general setting of essential actions studied in detail in Caprace and Sageev’s Rank Rigidity of CAT(0)-cube complexes and Sageev’s early work, the author proves that non-uniform lattices acting on CAT(0)-cube complexes with strict fundamental domain are not finitely generated- generalising the work of Thomas and Wortman in the case of non-uniform lattices of right-angled buildings. The final section is the construction of the quotient and complex of groups of SL2(F2[t, t−1 ]) acting on T3 × T3, the product of Bruhat-Tits trees corresponding to SL2(F2((t))) and SL2(F2((t −1 ))).
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Date
2021Rights statement
The author retains copyright of this thesis. It may only be used for the purposes of research and study. It must not be used for any other purposes and may not be transmitted or shared with others without prior permission.Faculty/School
Faculty of Science, School of Mathematics and StatisticsAwarding institution
The University of SydneyShare