논문KCI 등재
STRONG COHOMOLOGICAL RIGIDITY OF A PRODUCT OF PROJECTIVE SPACES
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초록
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) ${\Pi}_{i=1}^{m}\mathbb{C}P^{ni}{\rightarrow}M$.
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) ${\Pi}_{i=1}^{m}\mathbb{C}P^{ni}{\rightarrow}M$.
참고문헌 (6)
- S. Choi, "Quasitoric manifolds over a product of simplices", Osaka J. Math, 47(1), pp.1~21 (2010)
- 서동엽, "TOPOLOGICAL CLASSIFICATION OF GENERALIZED BOTT TOWERS", TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 362(2), pp.1097~1112, AMER MATHEMATICAL SOC
- S. Choi, "Rigidity problems in toric topology, a survey", Proc. Steklov Inst. Math
- M. W. Davis, "Convex polytopes, Coxeter orbifolds and torus ac- tions", Duke Math. J, 62(2), pp.417~451 (1991)
- R. Friedman, "On the diffeomorphism types of certain algebraic sur- faces. I", J. Differential Geom, 27(2), pp.297~369 (1988)
- M. Masuda, "Semi-free circle actions, Bott towers, and quasitoric man- ifolds", Mat. Sb, 199(8), pp.95~122 (2008)
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