Discussion of twists of KR-theory by HZR-theory in degree 3 via bundle gerbes (Jandl gerbes) suitable for classifying D-brane charge on orientifolds:
Pedram Hekmati, Michael Murray, Richard Szabo, Raymond Vozzo, Real bundle gerbes, orientifolds and twisted KR-homology, Advances in Theoretical and Mathematical Physics Volume 23 (2019) Number (arXiv:1608.06466, doi:10.4310/ATMP.2019.v23.n8.a5)
Pedram Hekmati, Michael Murray, Richard Szabo, Raymond Vozzo, Sign choices for orientifolds (arXiv:1905.06041)
On Donaldson-Thomas theory and Hilbert schemes:
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