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algebra analytic assume automorphic factor boundary bounded canonical coefficients cohomology group commutative compact complex vector space components condition consider contains converges coordinates Corollary corresponding curvature curve decomposition defined definition degree denote diam differential dimension divisor domain element of G equation exact sequence exists F-valued finite follows geodesic given harmonic forms Hence holomorphic holomorphic function homeomorphism homotopy equivalence identity implies induces inner product invariant involution isomorphism Lemma Let f Lie ring linear Math metric module morphism neighborhood non-degenerate norm normal subgroup notation obtain open set operator p-form polynomial positive integer positive number pre-Lie projection proof of Theorem Proposition prove quotient space representation resp respect result riemannian manifold ring satisfies semi-norm sheaf simplex simplicial structure subcomplex subset Suppose suspension-order tangent Theorem theory topological triangulation trivial unknotted vanishes vector bundle vector field vector space wchp