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On equivariant Grothendieck cohomology of a real algebraic variety, and its applications. (English. Russian original) Zbl 0843.14024
Russ. Acad. Sci., Izv., Math. 44, No. 3, 461-477 (1995); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 58, No. 3, 36-52 (1994).
New results on equivariant cohomology of a real algebraic variety are proved; in particular, the first spectral sequence is computed. These results are applied to prove analogues of the Harnack-Thom inequality and to study relations between characteristic classes.

MSC:
14P25 Topology of real algebraic varieties
18G40 Spectral sequences, hypercohomology
14F20 √Čtale and other Grothendieck topologies and (co)homologies
57R20 Characteristic classes and numbers in differential topology
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