L2 dimensions of spaces of braid-invariant harmonic forms

Mathematics – Functional Analysis

Scientific paper

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Scientific paper

Let X be a Riemannian manifold endowed with a co-compact isometric action of
an infinite discrete group. We consider L2 spaces of harmonic vector-valued
forms on the product manifold X^N, which are invariant with respect to an
action of the braid group B_N, and compute their von Neumann dimensions (the
braided L2- Betti numbers)

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