کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898245 | 1631334 | 2018 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Tractor calculus, BGG complexes, and the cohomology of cocompact Kleinian groups
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
For a compact, oriented, hyperbolic n-manifold (M,g), realised as M=Î\Hn where Î is a torsion-free cocompact subgroup of SO(n,1), we establish and study a relationship between differential geometric cohomology on M and algebraic invariants of the group Î. In particular for F an irreducible SO(n,1)-module, we show that the group cohomology with coefficients H
- (Î,F) arises from the cohomology of an appropriate projective BGG complex on M. This yields the geometric interpretation that H
- (Î,F) parameterises solutions to certain distinguished natural PDEs of Riemannian geometry, modulo the range of suitable differential coboundary operators. Viewed in another direction, the construction shows one way that non-trivial cohomology can arise in a BGG complex, and sheds considerable light on its geometric meaning. We also use the tools developed to give a new proof that H1(Î,S0kRn+1)â 0 whenever M contains a compact, orientable, totally geodesic hypersurface. All constructions use another result that we establish, namely that the canonical flat connection on a hyperbolic manifold coincides with the tractor connection of projective differential geometry.
- (Î,F) arises from the cohomology of an appropriate projective BGG complex on M. This yields the geometric interpretation that H
- (Î,F) parameterises solutions to certain distinguished natural PDEs of Riemannian geometry, modulo the range of suitable differential coboundary operators. Viewed in another direction, the construction shows one way that non-trivial cohomology can arise in a BGG complex, and sheds considerable light on its geometric meaning. We also use the tools developed to give a new proof that H1(Î,S0kRn+1)â 0 whenever M contains a compact, orientable, totally geodesic hypersurface. All constructions use another result that we establish, namely that the canonical flat connection on a hyperbolic manifold coincides with the tractor connection of projective differential geometry.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 61, December 2018, Pages 20-41
Journal: Differential Geometry and its Applications - Volume 61, December 2018, Pages 20-41
نویسندگان
A. Rod Gover, Callum Sleigh,