On equivariant ordinary differential cohomology:
Corbett Redden, Differential Borel equivariant cohomology via connections, New York Journal of Mathematics, Volume 23 (2017) 441-487 (nyjm:23-20, arXiv:1602.06921)
Corbett Redden, An alternate description of equivariant connections, Differential Geometry and its Applications Volume 56, February 2018, Pages 81-94 (doi:10.1016/j.difgeo.2017.11.003 arXiv:1608.01297)
Byungdo Park, Corbett Redden: A classification of equivariant gerbe connections, Communications in Contemporary Mathematics 21 02 (2019) 1850001 [doi:10.1142/S0219199718500013, arXiv:1709.06003]
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