Journal of Noncommutative Geometry

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Volume 12, Issue 1, 2018, pp. 69–106
DOI: 10.4171/JNCG/271

Published online: 2018-03-23

Hopf-dihedral (co)homology and $L$-theory

Atabey Kaygun[1] and Serkan Sütlü[2]

(1) Istanbul Technical University, Turkey
(2) Işık University, Istanbul, Turkey

We develop an appropriate dihedral extension of the Connes–Moscovici characteristic map for Hopf $\ast$-algebras. We then observe that one can use this extension together with the dihedral Chern character to detect non-trivial $L$-theory classes of a $\ast$-algebra that carry a Hopf symmetry over a Hopf $\ast$-algebra. Using our machinery we detect a previously unknown $L$-class of the standard Podleś sphere.

Keywords: Hopf $\ast$-algebras, $L$-theory, Chern character, Hopf-dihedral cohomology

Kaygun Atabey, Sütlü Serkan: Hopf-dihedral (co)homology and $L$-theory. J. Noncommut. Geom. 12 (2018), 69-106. doi: 10.4171/JNCG/271