Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2012; 49(4): 761-765

Printed July 1, 2012

https://doi.org/10.4134/BKMS.2012.49.4.761

Copyright © The Korean Mathematical Society.

Strong cohomological rigidity of a product of projective spaces

Suyoung Choi and Dong Youp Suh

Ajou University, KAIST

Abstract

We prove that for a toric manifold (respectively, a quasitoric manifold) $M$, any graded ring isomorphism $H^\ast(M) \to H^\ast(\prod_{i=1}^{m}\mathbb CP^{n_i})$ can be realized by a diffeomorphism (respectively, a homeomorphism) $\prod_{i=1}^m \mathbb CP^{n_i} \to M$.

Keywords: product of projective spaces, generalized Bott manifold, strong cohomological rigidity, toric manifold, quasitoric manifold

MSC numbers: Primary 57S25; Secondary 22F30

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