Abstract
Torus orbifolds are topological generalizations of symplectic toric orbifolds. The authours give a construction of smooth orbifolds with torus actions whose boundary is a disjoint union of torus orbifolds using a toric topological method. As a result, they show that any orientable locally standard torus orbifold is equivariantly cobordant to some copies of orbifold complex projective spaces. They also discuss some further equivariant cobordism results including the cases when torus orbifolds are actually torus manifolds.
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Acknowledgement
The first author thanks Indian Institute of Sciences, Pacific Institute for Mathematical Sciences and University of Regina for support. He also thanks Indian Statistical Institute, Kolkata and Institute of Mathematical Sciences for supporting his visiting fellowship. The authors would like to thank anonymous referee, Mainak Poddar and Nigel Ray for many helpful comments and suggestions.
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This work was supported by the National Research Foundation of Korea (NRF for short) grant funded by the Korea government (MSIP) (No. 2016R1A2B4010823).
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Sarkar, S., Suh, D. Equivariant Cobordism of Torus Orbifolds. Chin. Ann. Math. Ser. B 42, 861–890 (2021). https://doi.org/10.1007/s11401-021-0295-0
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DOI: https://doi.org/10.1007/s11401-021-0295-0