Abstract
This paper deals with two things. First, the cohomology of canonical extensions of real topological toric manifolds is computed when coefficient ring G is a commutative ring in which 2 is unit in G. Second, the author focuses on a specific canonical extensions called doublings and presents their various properties. They include existence of infinitely many real topological toric manifolds admitting complex structures, and a way to construct infinitely many real toric manifolds which have an odd torsion in their cohomology groups. Moreover, some questions about real topological toric manifolds related to Halperin’s toral rank conjecture are presented.
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Acknowledgments
The author is thankful to Suyoung Choi for all of helpful conversations and comments.
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Park, H. Wedge operations and doubling operations of real toric manifolds. Chin. Ann. Math. Ser. B 38, 1321–1334 (2017). https://doi.org/10.1007/s11401-017-1040-6
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DOI: https://doi.org/10.1007/s11401-017-1040-6
Keywords
- Real toric manifold
- Small cover
- Real topological toric manifold
- Coho-mology ring
- Doubling
- Simplicial wedge
- Rational homology sphere