group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
The twisted cohomology version of ordinary cohomology.
twisted Bredon cohomology (twisted ordinary equivariant cohomology)
Original articles:
Kurt Reidemeister, Überdeckungen von Komplexen, Crelle 173 (1935), 164-173 [doi:10.1515/crll.1935.173.164]
Norman Steenrod, Homology With Local Coefficients, Annals of Mathematics, Second Series, Vol. 44, No. 4 (Oct., 1943), pp. 610-627 (jstor:1969099)
Classification of twisted cohomology by fibrations/bundles of Eilenberg-MacLane spaces over the classifying space of a twisting group (universally: the fundamental group of the domain space):
Samuel Gitler, Cohomology operations with local coefficients, American Journal of Mathematics 85 2 (1963) 156–188 [doi:10.2307/2373208]
Yasumasa Hirashima, A note on cohomology with local coefficients, Osaka J. Math., 16 1 (1979) 219-231 &lbrackeuclid:ojm/1200771839]
Paul Goerss, J. F. Jardine, p. 332 of: Simplicial homotopy theory, Progress in Mathematics, Birkhäuser (1999) Modern Birkhäuser Classics (2009) [doi:10.1007/978-3-0346-0189-4]
M. Bullejos, E. Faro, M. A. García-Muñoz, Homotopy colimits and cohomology with local coefficients, Cahiers de Topologie et Géométrie Différentielle Catégoriques, 44 no. 1 (2003), p. 63-80 [numdam:CTGDC_2003__44_1_63_0]
Review:
Discussion as a special case of a more general notion of twisted non-abelian cohomology by -categorical hom-spaces in slice -toposes:
Thomas Nikolaus, Urs Schreiber, Danny Stevenson, Rem. 4.22 in: Principal -bundles – General Theory, Journal of Homotopy and Related Structures, 10 4 (2015) 749-801 [doi:10.1007/s40062-014-0083-6, arXiv:1207.0248]
Domenico Fiorenza, Hisham Sati, Urs Schreiber, Ex. 2.32 in: The Character Map in Twisted Non-Abelian Cohomology [arXiv:2009.11909]
Last revised on January 10, 2024 at 00:20:06. See the history of this page for a list of all contributions to it.