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<p>Quasitoric orbifolds and locally 1-standard <i>T</i>-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 (2<i>n</i> + 1)-dimensional smooth orientable manifold with <i>T</i><sup><i>n</i>+1</sup>-action whose boundary is a given locally 1-standard <i>T</i>-manifold. Moreover, they conclude that good contact toric manifolds and generalized lens spaces are equivariantly cobordant to zero.</p>

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

  • 期刊论文

  • 发表日期：

    2026年6月24日

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  • Koushik Brahma,
  • Soumen Sarkar,
  • Subhankar Sau

摘要

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.