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We characterize groups admitting Anosov representations into    SL  (  3  ,  R  )   , projective Anosov representations into    SL  (  4  ,  R  )   , and Borel Anosov representations into    SL  (  4  ,  R  )   . More generally, we obtain bounds on the cohomological dimension of groups admitting    P  k   ‐Anosov representations into    SL  (  d  ,  R  )    and offer several characterizations of Benoist representations.

Topological restrictions on Anosov representations