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- W2008873721 abstract "We study a Hopf algebroid, $calh$, naturally associated to the groupoid $U_n^deltaltimes U_n$. We show that classes in the Hopf cyclic cohomology of $calh$ can be used to define secondary characteristic classes of trivialized flat $U_n$-bundles. For example, there is a cyclic class which corresponds to the universal transgressed Chern character and which gives rise to the continuous part of the $rho$-invariant of Atiyah-Patodi-Singer. Moreover, these cyclic classes are shown to extend to the K-theory of the associated $C^{*}$-algebra. This point of view gives leads to homotopy invariance results for certain characteristic numbers. In particular, we define a subgroup of the cohomology of a group analogous to the Gelfand-Fuchs classes described by Connes, cite{connes:transverse}, and show that the higher signatures associated to them are homotopy invariant." @default.
- W2008873721 created "2016-06-24" @default.
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- W2008873721 date "2007-11-20" @default.
- W2008873721 modified "2023-09-27" @default.
- W2008873721 title "Hopf algebroids and secondary characteristic classes" @default.
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