On cobordism of generalized (real) Bott manifolds

We show that all generalized (real) Bott manifolds which are (small covers) quasitoric manifolds over a product of simplices \(\Delta^{n_1}\times\cdots\times\Delta^{n_r}\times\Delta^{1}\) are always boundaries of some manifolds. But these manifolds with the natural \((\mathbb{Z}_2)^n\) action do not...

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Veröffentlicht in:arXiv.org 2017-10
1. Verfasser: Lu, Yuxiu
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Sprache:eng
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Zusammenfassung:We show that all generalized (real) Bott manifolds which are (small covers) quasitoric manifolds over a product of simplices \(\Delta^{n_1}\times\cdots\times\Delta^{n_r}\times\Delta^{1}\) are always boundaries of some manifolds. But these manifolds with the natural \((\mathbb{Z}_2)^n\) action do not necessarily bound equvariantly. In addition, we can construct some examples of null-cobordant but not orientedly null-cobordant manifolds among quasitoric manifolds.
ISSN:2331-8422