Browse > Article
http://dx.doi.org/10.4134/BKMS.2012.49.4.761

STRONG COHOMOLOGICAL RIGIDITY OF A PRODUCT OF PROJECTIVE SPACES  

Choi, Su-Young (Department of Mathematics Ajou University)
Suh, Dong-Youp (Department of Mathematical Sciences Korea Advanced Institute of Science and Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.4, 2012 , pp. 761-765 More about this Journal
Abstract
We prove that for a toric manifold (respectively, a quasitoric manifold) M, any graded ring isomorphism $H^*(M){\rightarrow}H^*({\Pi}_{i=1}^{m}\mathbb{C}P^{ni})$ can be realized by a diffeomorphism (respectively, a homeomorphism) ${\Pi}_{i=1}^{m}\mathbb{C}P^{ni}{\rightarrow}M$.
Keywords
product of projective spaces; generalized Bott manifold; strong cohomological rigidity; toric manifold; quasitoric manifold;
Citations & Related Records
 (Related Records In Web of Science)
연도 인용수 순위
  • Reference
1 S. Choi, M. Masuda, and D. Y. Suh, Quasitoric manifolds over a product of simplices, Osaka J. Math. 47 (2010), no. 1, 1-21.
2 S. Choi, M. Masuda, and D. Y. Suh, Topological classification of generalized Bott manifolds, Trans. Amer. Math. Soc. 362 (2010), no. 2, 1097-1112.
3 S. Choi, M. Masuda, and D. Y. Suh, Rigidity problems in toric topology, a survey, to appear in Proc. Steklov Inst. Math; arXiv:1102.1359.
4 M. W. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991), no. 2, 417-451.   DOI
5 R. Friedman and J. W. Morgan, On the diffeomorphism types of certain algebraic surfaces. I, J. Differential Geom. 27 (1988), no. 2, 297-369.
6 M. Masuda and T. E. Panov, Semi-free circle actions, Bott towers, and quasitoric manifolds, Mat. Sb. 199 (2008), no. 8, 95-122.   DOI