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3-manifold abelian Abstracts algebra algorithm analysis analytic applications asymptotic automorphism Banach space boundary bounded braid groups classical coefficients compact complex conjecture construction convergence convex convex sets curvature decomposition defined denote Department of Mathematics derivatives differential equations dimension dimensional discuss domain equivalent exists field finite formula functions geometric given graph Hilbert space holomorphic homeomorphic homotopy ideal inequality infinite integer integral invariant irreducible isomorphic knot lattice Lie algebra Lie group linear manifold Math matrix method metric metric space minimal module nonlinear norm obtained operators p-adic paper partial differential equations polynomial Preliminary report prime proof properties prove Radon transform Received August Received February Received January Received July Received October 15 Received September representations Riemannian manifold ring satisfies semigroup sequence singular solutions Sponsored structure subgroup subset subspace surfaces symmetric Texas Theorem theory topology transform University variables vector zero