Journal of the Mathematical Society of Japan

Equivariant weight filtration for real algebraic varieties with action


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We show the existence of a weight filtration on the equivariant homology of real algebraic varieties equipped with a finite group action, by applying group homology to the weight complex of McCrory and Parusiński. If the group is of even order, we can not extract additive invariants directly from the induced spectral sequence.

Nevertheless, we construct finite additive invariants in terms of bounded long exact sequences, recovering Fichou's equivariant virtual Betti numbers in some cases. In the case of the two-elements group, we recover these additive invariants by using globally invariant chains and the equivariant version of Guillén and Navarro Aznar's extension criterion.

Article information

J. Math. Soc. Japan Volume 68, Number 4 (2016), 1789-1818.

First available in Project Euclid: 24 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14P25: Topology of real algebraic varieties
Secondary: 14P10: Semialgebraic sets and related spaces 57S17: Finite transformation groups 57S25: Groups acting on specific manifolds

equivariant homology weight filtration real algebraic varieties group action additive invariants


PRIZIAC, Fabien. Equivariant weight filtration for real algebraic varieties with action. J. Math. Soc. Japan 68 (2016), no. 4, 1789--1818. doi:10.2969/jmsj/06841789.

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