Abstract
We prove that the higher harmonic signature of an even dimensional oriented Riemannian foliation $F$ of a compact Riemannian manifold $M$ with coefficients in a leafwise $U(p, q)$-flat complex bundle is a leafwise homotopy invariant. We also prove the leafwise homotopy invariance of the twisted higher Betti classes. Consequences for the Novikov conjecture for foliations and for groups are investigated.
Citation
Moulay-Tahar Benameur. James L. Heitsch. "The twisted higher harmonic signature for foliations." J. Differential Geom. 87 (3) 389 - 468, March 2011. https://doi.org/10.4310/jdg/1312998231
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