Authors: | Baralić, Đorđe Milenković, Lazar |
Affiliations: | Mathematics Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | Small Covers and Quasitoric Manifolds over Neighborly Polytopes | Journal: | Mediterranean Journal of Mathematics | Volume: | 19 | Issue: | 2 | First page: | 87 | Issue Date: | 1-Apr-2022 | Rank: | ~M21 | ISSN: | 1660-5446 | DOI: | 10.1007/s00009-022-01989-5 | Abstract: | We prove that the duals of neighborly simplicial n-polytopes with the number of vertices greater than 2⌈n2⌉+2+[n2]-3 cannot appear as the orbit spaces of a small cover for all n∈ N. We investigate small covers and quasitoric manifolds over the duals of neighborly simplicial polytopes with small number of vertices in dimensions 4, 5, 6 and 7. In most of the considered cases, we obtain the complete classification of small covers. The lifting conjecture in all cases is verified to be true. The problem of C-rigidity for small covers is also studied and we have found a whole new series of ‘exceptional’ polytopes, which are polytopes such that small covers over them are classified up to a homeomorphism by their graded Z2-cohomology rings. New examples of manifolds provide the first known examples of quasitoric manifolds in higher dimensions whose orbit polytopes have chromatic numbers χ(Pn) ≥ 3 n- 5. |
Keywords: | neighborly polytopes | quasitoric manifolds | Small covers | the classification problem | the lifting conjecture | Publisher: | Springer Link |
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