Journal of the Mathematical Society of Japan

Equivariant weight filtration for real algebraic varieties with action

Fabien PRIZIAC

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Abstract

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

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

Dates
First available in Project Euclid: 24 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1477327234

Digital Object Identifier
doi:10.2969/jmsj/06841789

Mathematical Reviews number (MathSciNet)
MR3564452

Zentralblatt MATH identifier
06669098

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

Keywords
equivariant homology weight filtration real algebraic varieties group action additive invariants

Citation

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. https://projecteuclid.org/euclid.jmsj/1477327234


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