Equivariant cohomological rigidity of certain T–manifolds

Resolution of singularities of quasitoric orbifolds and equivariant cobordism of quasi-contact toric manifolds

“…Note that p2n `1q-dimensional quasi-contact toric manifolds are locally 1-standard T n,1 -manifolds of [SS21]. Let q : N Ñ P be the orbit map where P is an n-dimensional simple polytope.…”

“…In [SS21] the constructive definition of p2n `1q-dimensional quasi-contact toric manifolds on simple polytope has been discussed. Let FpP q :" tF 1 , .…”

“…Recently, in [SS21], the construction of toric manifolds in [DJ91] has been extended to introduce the notion of locally k-standard T n -manifold. In particular, the authors in [SS21] consider the invariant subset C n ˆS1 of C n`1 with respect to the standard T n`1 -action, and called the restricted T n`1 action on C n ˆS1 as the local model to define a locally standard T n,1 -manifold.…”

“…Recently, in [SS21], the construction of toric manifolds in [DJ91] has been extended to introduce the notion of locally k-standard T n -manifold. In particular, the authors in [SS21] consider the invariant subset C n ˆS1 of C n`1 with respect to the standard T n`1 -action, and called the restricted T n`1 action on C n ˆS1 as the local model to define a locally standard T n,1 -manifold. Briefly, a p2n `1q-dimensional smooth compact T n`1 -manifold M is called a quasi-contact toric manifolds if each point of M has an invariant neighbourhood which is diffeomorphic to an invariant open subset of C n ˆS1 , such that the orbit space M {T n`1 has the structure of a simple polytope.…”

“…The article [SS21] shows that the category of quasi-contact toric manifolds contains all good contact toric manifolds.…”