TY - GEN
T1 - Enumerating Kleinian Groups
AU - Gabai, David
AU - Meyerhoff, Robert
AU - Thurston, Nathaniel
AU - Yarmola, Andrew
N1 - Publisher Copyright:
© 2023 American Mathematical Society.
PY - 2023
Y1 - 2023
N2 - In this manuscript, we give an overview of the tools and techniques needed for successfully classifying “low-complexity” Kleinian groups. In particular, we focus on extracting topological and geometric properties of discrete Kleinian groups, such as bounds on tube radii, cusp geometry, volume, relators in group presentation, and similar quantities. A key point of this manuscript is to explain how a discrete set of solutions (or their closure) can be found using continuous methods, in particular by searching over a continuous parameter space of groups. These methods provide an effective avenue for studying and classifying hyperbolic 3-manifolds that satisfy some geometric or topological constraints.
AB - In this manuscript, we give an overview of the tools and techniques needed for successfully classifying “low-complexity” Kleinian groups. In particular, we focus on extracting topological and geometric properties of discrete Kleinian groups, such as bounds on tube radii, cusp geometry, volume, relators in group presentation, and similar quantities. A key point of this manuscript is to explain how a discrete set of solutions (or their closure) can be found using continuous methods, in particular by searching over a continuous parameter space of groups. These methods provide an effective avenue for studying and classifying hyperbolic 3-manifolds that satisfy some geometric or topological constraints.
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U2 - 10.1090/conm/783/15744
DO - 10.1090/conm/783/15744
M3 - Conference contribution
AN - SCOPUS:85152923319
SN - 9781470468040
T3 - Contemporary Mathematics
SP - 1
EP - 25
BT - Computational Aspects of Discrete Subgroups of Lie Groups
A2 - Detinko, Alla
A2 - Kapovich, Michael
A2 - Kontorovich, Alex
A2 - Sarnak, Peter
A2 - Schwartz, Richard
PB - American Mathematical Society
T2 - Virtual Conference on Computational Aspects of Discrete Subgroups of Lie Groups, 2021
Y2 - 14 June 2021 through 18 June 2021
ER -