Resolution of Singularities of Quasitoric Orbifolds and Equivariant Cobordism of Certain T-manifolds

Abstract

Quasitoric orbifolds and locally 1-standard T-manifolds are the topological generalizations of simplicial projective toric varieties and good contact toric manifolds respectively. In this paper, the authors show that there is a resolution of singularities of a quasitoric orbifold. Then, they give an explicit construction of a (2n + 1)-dimensional smooth orientable manifold with Tⁿ⁺¹-action whose boundary is a given locally 1-standard T-manifold. Moreover, they conclude that good contact toric manifolds and generalized lens spaces are equivariantly cobordant to zero.

Keywords

Resolution of singularity / Quasitoric orbifold / Torus action / Locally 1-standard T-manifold / Equivariant cobordism / 14E15 / 57R85 / 52B11 / 57S12

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