English

On cobordism of generalized (real) Bott manifolds

Algebraic Topology 2017-10-03 v1

Abstract

We show that all generalized (real) Bott manifolds which are (small covers) quasitoric manifolds over a product of simplices Δn1××Δnr×Δ1\Delta^{n_1}\times\cdots\times\Delta^{n_r}\times\Delta^{1} are always boundaries of some manifolds. But these manifolds with the natural (Z2)n(\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.

Keywords

Cite

@article{arxiv.1710.00562,
  title  = {On cobordism of generalized (real) Bott manifolds},
  author = {Yuxiu Lu},
  journal= {arXiv preprint arXiv:1710.00562},
  year   = {2017}
}