Non-commutative analytic torsion form on the transformation groupoid convolution algebra
Given a fiber bundle $Z \to M \to B$ and a flat vector bundle $E \to M$ with a compatible action of a discrete group $G$, and regarding $B / G$ as the non-commutative space corresponding to the crossed product algebra, we construct an analytic torsion form as a non-commutative deRham differential fo...
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Zusammenfassung: | Given a fiber bundle $Z \to M \to B$ and a flat vector bundle $E \to M$ with
a compatible action of a discrete group $G$, and regarding $B / G$ as the
non-commutative space corresponding to the crossed product algebra, we
construct an analytic torsion form as a non-commutative deRham differential
form. We show that our construction is well defined under the weaker assumption
of positive Novikov-Shubin invariant. We prove that this torsion form appears
in a transgression formula, from which a non-commutative
Riamannian-Roch-Grothendieck index formula follows. |
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DOI: | 10.48550/arxiv.1701.04513 |