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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Infinitesimal rigidity for the action of $ {\rm SL}(n,{\bf Z})$ on $ {\bf T}\sp n$


Author: James W. Lewis
Journal: Trans. Amer. Math. Soc. 324 (1991), 421-445
MSC: Primary 22E40
DOI: https://doi.org/10.1090/S0002-9947-1991-1058434-X
MathSciNet review: 1058434
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Abstract: Let $ \Gamma = {\mathbf{SL}}(n,\mathbb{Z})$ or any subgroup of finite index. Then the action of $ \Gamma$ on $ {\mathbb{T}^n}$ by automorphisms is infinitesimally rigid for $ n \ge 7$, i.e., the cohomology $ {\text{H}^1}(\Gamma ,\operatorname{Vec} ({\mathbb{T}^n})) = 0$, where $ \operatorname{Vec} ({\mathbb{T}^n})$ denotes the module of $ {C^\infty }$ vector fields on $ {\mathbb{T}^n}$.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1058434-X
Article copyright: © Copyright 1991 American Mathematical Society