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\(L^ p\)-cohomology: Banach spaces and homological methods on Riemannian manifolds. (English) Zbl 0805.55006

Greene, Robert (ed.) et al., Differential geometry. Part 2: Geometry in mathematical physics and related topics. Proceedings of a summer research institute, held at the University of California, Los Angeles, CA, USA, July 8-28, 1990. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 54, Part 2, 637-655 (1993).
The author reports on the definition and general feature of \(L^ p\)- cohomology for Riemannian manifolds. The second part of the paper contains results on the \(L^ 2\)-cohomology in the case of Poincaré metrics, conical singularities, Fubini-Study metrics on projective varieties and locally-symmetric varieties.
For the entire collection see [Zbl 0773.00023].

MSC:

55N35 Other homology theories in algebraic topology
58A12 de Rham theory in global analysis
58J40 Pseudodifferential and Fourier integral operators on manifolds
55N33 Intersection homology and cohomology in algebraic topology
58A14 Hodge theory in global analysis
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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