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The cohomology rings of real toric spaces and smooth real toric varieties

Part of: Classical Topics in Algebraic Topology Special varieties (Co)homology theory

Published online by Cambridge University Press:  29 June 2021

Matthias Franz
Matthias Franz*
Affiliation:
Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada ([email protected])
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Abstract

We compute the cohomology rings of smooth real toric varieties and of real toric spaces, which are quotients of real moment-angle complexes by freely acting subgroups of the ambient 2-torus. The differential graded algebra (dga) we present is in fact an equivariant dga model, valid for arbitrary coefficients. We deduce from our description that smooth toric varieties are $\hbox{M}$-varieties.

Keywords

Real toric spacereal toric varietymaximal varietydga modelface coalgebra

MSC classification

Primary: 14M25: Toric varieties, Newton polyhedra
Secondary: 14F45: Topological properties 55M35: Finite groups of transformations (including Smith theory)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 3 , June 2022 , pp. 720 - 737
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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