On Cheeger-Simons differential characters and secondary invariants:
On Ricci curvature:
Michael T. Anderson, Jeff Cheeger, -compactness for manifolds with Ricci curvature and injectivity radius bounded below J. Diff. Geo. 35 2 (1992) 265-281 [doi:10.4310/jdg/1214448075]
Jeff Cheeger, Aaron Naber: Lower bounds on Ricci curvature and quantitative behavior of singular sets, Invent. Math. 191 (2013) 321–339 [arXiv:1103.1819, doi:10.1007/s00222-012-0394-3]
On special holonomy orbifolds:
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