Higher cohomology of parabolic actions on certain homogeneous spaces

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JournalJournal d'Analyse Mathématique
DateIn preparation - 14 Dec 2013
DateAccepted/In press - 14 Aug 2014
DateE-pub ahead of print - 4 Apr 2017
DatePublished (current) - 2017
Issue number1
Volume131
Pages (from-to)255-275
Early online date4/04/17
Original languageEnglish

Abstract

We show that for a parabolic R^d-action on a compact quotient of PSL(2,R)^d, the cohomologies in degrees 1 through d-1 trivialize, and we give the obstructions to solving the degree-d coboundary equation, along with bounds on Sobolev norms of primitives. In previous papers we have established these results for certain Anosov systems. The present work extends the methods of those papers to systems that are not Anosov. The main new idea is in Section 4, where we define special elements of representation spaces that allow us to modify the arguments from the previous papers. In Section 7 we discuss how one may generalize this strategy to R^d-systems coming from a product of Lie groups, like in the systems we have here.

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© Hebrew University Magnes Press 2017. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

    Research areas

  • math.DS

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