Wedge operations and doubling operations of real toric manifolds.

*(English)*Zbl 1387.57040Summary: This paper deals with two things. First, the cohomology of canonical extensions of real topological toric manifolds is computed when the coefficient ring \(G\) is a commutative ring in which 2 is a unit. Second, the author focuses on 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.

##### MSC:

57N65 | Algebraic topology of manifolds |

57S17 | Finite transformation groups |

05E45 | Combinatorial aspects of simplicial complexes |

##### Keywords:

real toric manifold; small cover; real topological toric manifold; cohomology ring; doubling; simplicial wedge; rational homology sphere
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\textit{H. Park}, Chin. Ann. Math., Ser. B 38, No. 6, 1321--1334 (2017; Zbl 1387.57040)

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##### References:

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