The Extended Bloch Group and the Cheeger-Chern-Simons Class
S. Goette, C. Zickert
TL;DR
This paper provides a comprehensive formula for the Cheeger-Chern-Simons class of a specific flat complex vector bundle, improving previous formulas by accounting for the full class beyond modulo 2-torsion.
Contribution
It introduces an explicit formula for the full Cheeger-Chern-Simons class of the tautological flat bundle over BSL(2,C), extending prior work that only computed it modulo 2-torsion.
Findings
Derived a complete formula for the Cheeger-Chern-Simons class
Enhanced previous formulas by removing 2-torsion limitations
Applied the formula to the tautological flat bundle over BSL(2,C)
Abstract
We present a formula for the full Cheeger-Chern-Simons class of the tautological flat complex vector bundle of rank two over BSL(2,\C^\delta). Our formula improves the formula by Dupont and Zickert, where the class is only computed modulo 2-torsion.
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