The Combinatorial Description of the Highest Dimensional Cohomology Generators of Quasitoric-manifolds and Its Applications
For any quasitoric-manifold,π:M2n → Pn,its cohomology ring is ex-pressed as H*(M2n,Z)=Z[Fi,F2,…,Fm]/(IPn+JPn),where F(P)={F1,F2,…,Fm} is the set of all co-one-dimensional surfaces in Pn.Taking any vertex v=Fi1 ∩ Fi2 ∩… ∩ Fin of Pn,we prove that<[Fi1Fi2…Fin],[M2n]>=±1,that is,[Fi1Fi2 … Fin]is the generator of H2n(M2n,Z).Further we use this conclusion to discuss the rigidity of quasitoric-manifolds,and prove the following conclusions:If f*:H*(M2n1,Z)→ H*(M2n2,Z)is a ring isomorphism,then there exists a one-to-one mapping(f):Fix(M2n1)→ Fix(M2n2),where Fix(M2n)is the fixed point of Tn-acting on M2n.
Quasitoric manifoldindicative functioncohomology ring
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