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The weight filtration for real algebraic varieties II: classical homology

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

We associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on classical (compactly supported) homology with \(\mathbb Z _2\) coefficients an analog of the weight filtration for complex algebraic varieties. This complements our previous definition of the weight filtration of Borel–Moore homology.

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Authors and Affiliations

  1. Mathematics Department, University of Georgia, Athens, GA, 30602, USA

    Clint McCrory

  2. Laboratoire J.A. Dieudonné UMR CNRS 7351, Université de Nice-Sophia Antipolis, Parc Valrose, 06108 , Nice Cedex 02, France

    Adam Parusiński

Authors
  1. Clint McCrory
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  2. Adam Parusiński
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Correspondence to Adam Parusiński.

Additional information

To Heisuke Hironaka on the occasion of his 80th birthday.

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McCrory, C., Parusiński, A. The weight filtration for real algebraic varieties II: classical homology. RACSAM 108, 63–94 (2014). https://doi.org/10.1007/s13398-012-0098-y

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  • DOI: https://doi.org/10.1007/s13398-012-0098-y

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