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Mathematics  2014 

Complex Cobordism of quasitoric orbifolds

DOI: 10.1016/j.topol.2015.08.020

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Abstract:

We construct manifolds and orbifolds with quasitoric boundary. We show that these manifolds and orbifolds with boundary has a stable complex structure. These induce explicit (orbifold) complex cobordism relations among quasitoric manifolds and orbifolds. In particular, we show that a quasitoric orbifold is complex cobordant to some copies of fake weighted projective spaces. The famous problem of Hirzebruch is that which complex cobordism classes in $\Omega^U$ contain connected nonsingular algebraic varieties? We give some sufficient conditions to show when a complex cobordism class may contains an almost complex quasitoric manifold. Andrew Wilfong give some necessary condition of this problem up to dimension 8.

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