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| Wedge Operations and Doubling Operations of Real Toric Manifolds |
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Citation： |
Hanchul PARK.Wedge Operations and Doubling Operations of Real Toric Manifolds[J].Chinese Annals of Mathematics B,2017,38(6):1321~1334 |
| Page view： 1106
Net amount： 1263 |
Authors： |
Hanchul PARK; |
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| 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. |
Keywords： |
Real toric manifold, Small cover, Real topological toric manifold, Coho-
mology ring, Doubling, Simplicial wedge, Rational homology sphere |
Classification： |
57N65, 57S17, 05E45 |
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