### Nonzero degree tangential maps between dual symmetric spaces.

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Let W be a Coxeter group and let μ be an inner product on the group algebra ℝW. We say that μ is admissible if it satisfies the axioms for a Hilbert algebra structure. Any such inner product gives rise to a von Neumann algebra ${}_{\mu}$ containing ℝW. Using these algebras and the corresponding von Neumann dimensions we define $L{\xb2}_{\mu}$-Betti numbers and an $L{\xb2}_{\mu}$-Euler charactersitic for W. We show that if the Davis complex for W is a generalized homology manifold, then these Betti numbers satisfy a version of Poincaré...

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