The Extended Bloch Group and the Cheeger–Chern–Simons Class

Abstract

We present a formula for the full Cheeger–Chern–Simons class of the tautological flat complex vector bundle of rank $2$ over $BSL\left(2,{ℂ}^{\delta }\right)$. This improves the formula by Dupont and Zickert [Geom. Topol. 10 (2006) 1347–1372], where the class is only computed modulo 2–torsion.