Abstract
A real toric manifold \(X^{\mathbb R}\) is said to be cohomologically rigid over \({\mathbb Z}_2\) if every real toric manifold whose \({\mathbb Z}_2\)-cohomology ring is isomorphic to that of \(X^{\mathbb R}\) is actually diffeomorphic to \(X^{\mathbb R}\). Not all real toric manifolds are cohomologically rigid over \({\mathbb Z}_2\). In this paper, we prove that the connected sum of three real projective spaces is cohomologically rigid over \({\mathbb Z}_2\).
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The work was supported by the National Research Foundation of Korea, project no. NRF-2019R1A2C2010989.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Vol. 317, pp. 198–209 https://doi.org/10.4213/tm4285.
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Choi, S., Vallée, M. Cohomological Rigidity of the Connected Sum of Three Real Projective Spaces. Proc. Steklov Inst. Math. 317, 178–188 (2022). https://doi.org/10.1134/S0081543822020109
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DOI: https://doi.org/10.1134/S0081543822020109