# On the conservation of (equivariant) homeomorphism classes of M(J)-manifolds

# On the conservation of (equivariant) homeomorphism classes of M(J)-manifolds

A /toric manifold / is a closed manifold of dimension 2n which admits a locally standard half dimensional torus action whose orbit space can be identified with an n-dimensional simple polytope. Since it has a group action, we can classify the category of toric manifolds up to (i)homeomorphism, (ii) equivariant homeomorphism and (iii) equivalence (in the sense of Davis- Januszkiewicz). On the other hand, for a positive integral vector J=(j_1, ... , j_m), A. Bahri, M. Bendersky, F. R. Cohen and S. Gitler introduced one interesting way to construct a new toric manifold, say M(J), from M. In this talk, we investigate whether equivalent or (equivariant) homeomorphism classes of toric manifolds are conserved by this construction. More precisely, we answer whether two (equivariant) homeomorphic or equivalent toric manifolds give the (equivariant) homeomorphic or equivalent toric manifolds or not.