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

Citation:

Koushik BRAHMA ·,Soumen SARKAR ·,Subhankar SAU.Resolution of Singularities of Quasitoric Orbifolds and Equivariant Cobordismof Certain T-manifolds[J].Chinese Annals of Mathematics B,2026,(5):855~870
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Authors:

Koushik BRAHMA ·; Soumen SARKAR ·;Subhankar SAU

Foundation:

the Science and Engineering Research Board India.
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 T n+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

Classification:

14E15, 57R85, 52B11, 57S12
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