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L²-homology and reciprocity for right-angled Coxeter groups

Boris Okun, Richard Scott (2011)

Fundamenta Mathematicae

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 μ containing ℝW. Using these algebras and the corresponding von Neumann dimensions we define L ² μ -Betti numbers and an L ² μ -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...

Locally variational invariant field equations and global currents: Chern-Simons theories

Mauro Francaviglia, M. Palese, E. Winterroth (2012)

Communications in Mathematics

We introduce the concept of conserved current variationally associated with locally variational invariant field equations. The invariance of the variation of the corresponding local presentation is a sufficient condition for the current beeing variationally equivalent to a global one. The case of a Chern-Simons theory is worked out and a global current is variationally associated with a Chern-Simons local Lagrangian.

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